Ovulation and Fertile Window Calculator: a Window, Not a Day, and Why It Is Not Contraception

A predicted ovulation day and a fertile window, counted backwards from the next expected period because the luteal phase is the stable half of the cycle — with the window’s width shown first, the implantation range and an informative pregnancy-test date beside it, and the published typical-use failure rate of calendar methods stated plainly. This is a page for trying to conceive; it is not a way to avoid pregnancy.

Last updated 1 Oct 2026

These are estimates from dates and measurements, not findings about this pregnancy. A due date is a midpoint with weeks of normal variation either side, and a predicted fertile window is not a reliable way to avoid pregnancy. Nothing here replaces assessment by a midwife or doctor.

Predicted ovulation, and the window your own cycle variability implies

a period start date, cycle lengths and a luteal phase → predicted ovulation, the fertile window as dates, the next period, the implantation range and a test date

Year the last period startedThe first day of bleeding of your most recent period, which is cycle day 1. There is no clock in this calculator, so every date is one you type — which also means you can run it for a past cycle.

Month it startedThe month of that same first day. A list rather than a number because 03/04 means two different days on two sides of the world.

Day of the month it started1 to 31. A day that does not exist in the month you chose — 31 April, 29 February in a common year — is refused rather than rolled silently into the next month.

Usual cycle length in daysFirst day of one period to first day of the next. This drives the single headline figure. Across 612,613 logged ovulatory cycles the mean was 29.3 days with a standard deviation of 5.2, and the average woman’s own cycle length moved by 2.6 days from cycle to cycle — so a single number here is already an average of something that varies.

Shortest cycle over recent monthsIf you have tracked a few cycles, the shortest one. Together with the longest it produces a window rather than a day, which is the calendar method done properly rather than done confidently. If you only have one number, put it in both fields and read the note about what that costs you.

Longest cycle over recent monthsThe longest cycle over the same few months. Entered high and low the wrong way round, the page sorts them and says so rather than returning a window of negative width.

Luteal phase length in daysThe number of days from ovulation to the first day of the next period. 14 is the convention and the default, because the whole 280-day due-date rule is built on it. The large app-logged datasets put the real mean at 12.4 days with a standard deviation of 2.4 — less than half the variability of the follicular phase, which is exactly why counting backwards from the next period beats counting forwards from the last one.

14days after the first day of your last periodExample

a period that began on 9 March 2026, a usual cycle of 28 days, cycles running 26 to 31 days over recent months, and the conventional 14-day luteal phase

Count backwards from the next period, then take the measured six-day window around that point

ovulation, in days after the first day of bleeding: d_ov = C − L · as a cycle day: d_ov + 1 · next period: day 1 + C · fertile window from one cycle length: d_ov − 5 to d_ov · from your own range: (C_min − L − 5) to (C_max − L), width = (C_max − C_min) + 6 · Ogino 1923, in cycle days: (C_min − 18) to (C_max − 11) · implantation: d_ov + 6 to d_ov + 12 · test from: day 1 + C + 7 · due date if conception occurs: d_ov + 266

C: cycle length in days, first day of one period to first day of the next. Mean 29.3 with a standard deviation of 5.2 across 612,613 logged ovulatory cycles, and the average woman’s own cycle length moves by 2.6 days from cycle to cycle
L: luteal phase length: the days from ovulation to the first day of the next period. 14 is the convention and the default; the measured mean in the same dataset is 12.4 with a standard deviation of 2.4. Its standard deviation is less than half the follicular phase’s 5.3, which is the entire reason this page counts backwards
d_ov: days elapsed from the first day of bleeding to predicted ovulation. This is the headline. Elapsed days, not cycle day: the first day of bleeding is elapsed day 0 and cycle day 1, so the cycle day is d_ov + 1. At C = 28 and L = 14 that is 14 elapsed days and cycle day 15 — and 14 elapsed days is exactly what the 280-day due-date convention puts conception at
5: the number of days before ovulation on which conception was observed to be possible. Wilcox 1995 found conception only from intercourse in the six-day period ending on the day of ovulation, with probability rising from about 0.10 five days before to about 0.33 on the day itself. The day after ovulation carries an upper bound of 0.12 with an interval from zero — not excluded rather than demonstrated — and is not folded into the window here
(C_max − C_min) + 6: the width of the window your own cycle variability implies. The 6 is measured; everything above it is uncertainty about where ovulation lands. Putting the same number in both fields gives the minimum 6 and hides the uncertainty rather than removing it
266: days from ovulation to the estimated due date, which follows from the 280-day convention and conception at 14 days of gestational age. Checked against the due date page for every cycle length and start date tested

Worked example

a period that began on 9 March 2026, a usual cycle of 28 days, cycles running 26 to 31 days over recent months, and the conventional 14-day luteal phase
The headline. Ovulation is predicted at C − L = 28 − 14 = 14 days after the first day of bleeding. That is cycle day 15, because the first day of bleeding is cycle day 1 and elapsed day 0 — the single most common off-by-one in this subject. 14 elapsed days is also exactly where the 280-day due-date convention puts conception, which is how the two pages on this site stay consistent. As a date: 9 March 2026 plus 14 days is 23 March 2026, printed above as 20260323.
The window from one cycle length is six days. 18 to 23 March — five days before the predicted ovulation plus the day itself. That six-day span is the measured fertile period, not a prediction interval, and it is the narrowest honest answer available.
The window from your own range is eleven days, and that is the number to read. The shortest cycle of 26 puts ovulation at 26 − 14 = 12 days, so the window opens 12 − 5 = 7 days after day 1, which is 16 March 2026. The longest cycle of 31 puts it at 31 − 14 = 17 days, which closes the window on 26 March 2026. Width = (31 − 26) + 6 = 11 days. Five of those eleven days exist only because your cycles vary by five days, and no arithmetic removes them.
What Ogino's rule gives for the same two cycle lengths. First fertile cycle day = 26 − 18 = 8; last = 31 − 11 = 20. Thirteen days, overlapping this page's window but not identical to it: Ogino's numbers have a fixed 14-day luteal phase inside them, so set L to 12 here and this page's window moves while Ogino's does not. Knaus's version, minus 17 and minus 13, gives cycle days 9 to 18.
The rest of the cycle. The next period is expected 28 days after day 1, on 6 April 2026. If conception happens, implantation would be expected 6 to 12 days after ovulation — 20 to 26 days after day 1, so 29 March to 4 April, with a median around 1 April. A pregnancy test is printed for 13 April 2026, a week after the expected period: on 6 April itself about 10% of pregnancies are still undetectable by a highly sensitive test, and a week later that falls to 3% or less. And the due date, if conception occurs, is ovulation plus 266 days: 14 December 2026, which is also 9 March plus 280 days.
Now the part that matters most. The eleven-day window above is a prediction about where ovulation will fall, made from two numbers. In the one prospective study that estimated ovulation day directly, fewer than 30% of women had their fertile window fall entirely inside the conventional days 10 to 17 — and that held among women who called their cycles regular. On cycle day 7 about 17% of women are already inside their window; on every day from 6 to 21 the figure is at least 10%; 4 to 6% are still potentially fertile in the fifth week. Used to find days likely to produce a pregnancy, a wide window costs you nothing. Used the other way round, the same width is why about 24 in every 100 women relying on fertility awareness-based methods are pregnant within a year of typical use. The arithmetic on this page is exact; what it is arithmetic about is not.
And what the page refuses. Set the luteal phase to 18 and the cycle to 20 and ovulation would fall 2 days after the first day of bleeding: the page returns its incomplete message rather than that number, as it does for any combination putting ovulation fewer than 5 days in, including a luteal phase as long as the cycle. Enter 29 February 2026 and it refuses, because that date does not exist. Enter the longest cycle as 26 and the shortest as 31 and it sorts them and tells you it did.

What the calendar cannot see: chance of being inside the fertile window, by cycle day

Day-specific estimates from Wilcox, Dunson and Baird (BMJ 2000), 221 women and 696 cycles with ovulation estimated from daily hormone measurement. The conclusion the authors drew from the same data: only about 30% of women had a fertile window falling entirely inside days 10 to 17, and that was true among women who described their cycles as regular. This is the table to read before treating any predicted window as protection.
Cycle day	Probability of being in the fertile window	What that means for a calendar
4	about 2%	almost never fertile, and the only part of the cycle where that is close to true
7	about 17%	one woman in six is already in her window a week in
12 to 13	about 54% (the peak)	even at the peak it is barely better than a coin toss
6 to 21	at least 10% on every single day	sixteen consecutive days on which the chance is never negligible
30 and beyond	4 to 6%	a twentieth of women are still potentially fertile in the fifth week

Day-specific probability of conception, relative to ovulation

From Wilcox, Weinberg and Baird (NEJM 1995), 221 women and 625 cycles. Conception occurred only when intercourse took place in the six-day period ending on the day of ovulation. The two bracketing rows are upper confidence bounds the authors could not rule out, with the interval running from zero — which is why the familiar “five days before to one day after” is six observed days plus one that was never shown to be fertile.
Day relative to ovulation	Probability of conception from intercourse that day	Status of the evidence
7 days before	up to 0.12, interval from 0	not excluded, not demonstrated
5 days before	about 0.10	observed
4 to 2 days before	about 0.14 to 0.27	observed
1 day before	about 0.31	observed
day of ovulation	about 0.33	observed — the peak
1 day after	up to 0.12, interval from 0	not excluded, not demonstrated
2 or more days after	no conceptions observed	observed

The two calendar rules, side by side, for a cycle running 26 to 31 days

All three use the same two inputs and disagree, because each bakes in different assumptions about the luteal phase and about how long sperm survive. None is a measurement of a particular person. Changing the luteal phase on this page moves the third row and leaves the other two where they are, which is a fair picture of how much of this is convention.
	First fertile cycle day	Last fertile cycle day	Width
Ogino 1923 (shortest − 18, longest − 11)	8	20	13 days
Knaus 1929 (shortest − 17, longest − 13)	9	18	10 days
This page, from the measured six-day window and a 14-day luteal phase	8	18	11 days

A page for trying to conceive, what the legacy “safe period” framing got wrong, and what a calendar cannot see

This page is for people trying to conceive, and it absorbs a page that used to be called a “safe period calculator”. That name was a promise the arithmetic cannot keep. The same calculation — predict ovulation, mark the days around it — can be read two ways, and the two readings are not symmetrical. Used to find the days most likely to produce a pregnancy, a wide window is a mild inconvenience: you have more days than you needed. Used to find days on which to avoid one, the same width is a hole, because every day the prediction gets wrong in the direction of fertility is a day of false confidence. The numbers say how large the hole is. CDC’s contraceptive effectiveness table puts fertility awareness-based methods at 24 unintended pregnancies per 100 women in the first year of typical use — roughly one user in four, which is worse than almost everything else on that table. A systematic review of 53 studies of these methods found typical-use rates spanning 10 to 33 pregnancies per 100 users a year, and graded none of the 53 studies as high quality: zero high, 21 moderate, 32 low. So the phrase “safe days” is named here once, to say what is wrong with it, and is not used as a framing anywhere else on the page.

The one genuinely useful idea on a page like this is that you should count backwards, not forwards. A cycle has two halves, and they are not equally variable. Across 612,613 ovulatory cycles logged by 124,648 users, the follicular phase — first day of bleeding to ovulation — averaged 16.9 days with a standard deviation of 5.3, while the luteal phase — ovulation to the next period — averaged 12.4 days with a standard deviation of 2.4. The luteal half varies less than half as much as the follicular half. That is why ovulation is predicted here as the cycle length minus the luteal phase, which is a backwards count from the next expected period, rather than as a fixed “day 14” forwards from the last one. It is also why a long cycle does not mean a long luteal phase: in the same dataset the mean follicular phase ran from 10.4 days in cycles of 15 to 20 days up to 26.8 days in cycles of 36 to 50, while the luteal phase barely moved. Stretch is almost all in the first half.

The window has a measured width, and the measurement is narrower than people assume. In the Early Pregnancy Study, 221 women contributed 625 cycles in which the day of ovulation could be estimated from daily urinary hormone measurement. Conception occurred only when intercourse took place during a six-day period ending on the estimated day of ovulation. The day-specific probability of conception rose from about 0.10 five days before ovulation to about 0.33 on the day itself. That is the evidence base for the figure everyone quotes, and it is worth being precise about what it does and does not establish: the authors could not exclude a probability of conception of up to 0.12 on the seventh day before ovulation or on the day after it, with a confidence interval running from zero. So the commonly repeated “five days before to one day after” is six days of demonstrated fertility plus one day that could not be ruled out. This page gives the six-day window and names the extra day as what it is — not excluded, rather than shown.

What the method cannot see, stated as a number. The same study published day-specific estimates of the chance that a woman is inside her fertile window on each cycle day. On day 4 it is about 2%; it rises to about 17% by day 7 and peaks at about 54% on days 12 and 13; on every day from 6 to 21 it is at least 10%; and 4 to 6% of women are still potentially fertile in the fifth week of a cycle. The conclusion the authors drew is the one that matters here: only about 30% of women had a fertile window falling entirely within days 10 to 17, the range clinical guidance conventionally names — and that held among women who described their cycles as regular. Ovulation moves. A predicted window is a prediction about a moving target made from two numbers, and no amount of arithmetic narrows it. Methods that observe something are different in kind: a luteinising hormone test detects a surge that has happened, a waking temperature records a shift that has happened, cervical mucus changes with oestrogen that is actually circulating. All three are observations of this cycle; a calendar is a summary of previous ones.

Ogino’s rule, printed beside the modern window, because it is still what most “calendar method” advice means. Kyusaku Ogino published it in 1923: the first fertile day is the shortest recent cycle minus 18 and the last is the longest minus 11, counted in cycle days. Hermann Knaus arrived independently at minus 17 and minus 13. Ogino’s numbers have a fixed 14-day luteal phase inside them — 18 is 14 plus four days of sperm survival, 11 is 14 minus three — which is why the rule drifts away from the window on this page as soon as you change the luteal phase from 14. Neither is a measurement of you. They are printed together so the difference is visible, and because a reader who has been given “day 8 to day 20” by a leaflet should be able to see where that came from.

The secondary dates, and what each one’s uncertainty is. Implantation is shown as a range because it is one: in the same cohort, implantation occurred 6 to 12 days after ovulation, with a median around day 9. The pregnancy test date is shown as one week after the expected period rather than on the day of it, and the reason is a specific published finding — even with a highly sensitive test, about 10% of pregnancies are not detectable on the first day after a missed period, because the embryo has not yet implanted and produced enough hCG; waiting about a week brings false negatives down to 3% or less. A negative test before the expected period means very little. This page cannot confirm a pregnancy, cannot exclude one, and does not try: what it prints is a date from which a test starts being informative. For what a measured hCG does over time, that is the hCG doubling time page, which is a laboratory calculation and not a prediction.

Where this page ends and others begin. It predicts, from dates. It does not assess fertility, does not interpret a hormone result, and is not a diagnosis of anything. Ovarian reserve on an AMH result is the AMH age percentile interpreter; cycles that are long or absent for a reason belong with the Rotterdam PCOS criteria page; a mid-luteal progesterone, which is one of the few cheap ways to find out whether ovulation happened at all, is converted on the progesterone converter; and the male half of the question, which half of couples trying to conceive never get tested for, is the semen analysis interpreter and the total motile sperm count page. If conception does happen, the due date comes from the due date and gestational age page, and the two pages share one convention on purpose: the due date printed above is ovulation plus 266 days, which is identical to that page’s cycle-adjusted 280-day rule for every cycle length and every start date, whenever the luteal phase is 14. That was checked exhaustively rather than assumed, because two pages that disagree about the same cycle would be worse than one page that is wrong.

Frequently asked questions

Can I use this to work out which days are safe to have unprotected sex?

No, and the page is built so that it cannot be read that way. The figure to hold on to is CDC’s: about 24 women in every 100 using fertility awareness-based methods to avoid pregnancy become pregnant in the first year of typical use. That is roughly one in four, and the systematic review evidence underneath it is weak — 53 studies, none rated high quality, typical-use rates spanning 10 to 33 per 100 users a year. The structural reason is that this calculation predicts where a window probably is, and it is wrong in the fertile direction often enough to matter: fewer than 30% of women have their fertile window entirely inside the conventional days 10 to 17. For avoiding pregnancy, the methods that work are the ones on CDC’s table with single-digit or sub-1% typical-use failure rates, and the conversation to have is with a clinician rather than a calculator.

Why does the page count back from the next period instead of forward to day 14?

Because the second half of the cycle is the stable half. In 612,613 logged ovulatory cycles the luteal phase averaged 12.4 days with a standard deviation of 2.4, while the follicular phase averaged 16.9 days with a standard deviation of 5.3. Counting forwards from the last period ties your estimate to the variable half; counting backwards from the next expected period ties it to the stable half. The catch, and it is a real one, is that counting backwards needs a next period you have not had yet — so the prediction inherits the error in your cycle length as well. That is why the page asks for a shortest and a longest and gives you a window.

Is ovulation on day 14 or 15 of a 28-day cycle?

Both answers are in print and they differ by one day, because two different things are being counted. The first day of bleeding is cycle day 1, and it is also day 0 of elapsed time. The due-date convention is explicit that conception sits at 14 days of gestational age — that is why the due date is 280 days after the first day of the period and 266 days after conception, and why a day-5 embryo transfer gives 261. Fourteen days of elapsed time after cycle day 1 is cycle day 15. Meanwhile “ovulation on day 14” treats 14 as the cycle day. This page reports the elapsed count as its headline, gives the cycle day as that number plus one in the row beneath it, and keeps the 280-day identity intact, because every gestational age you will be quoted later depends on it.

What is the luteal phase and how do I know mine?

It is the stretch from ovulation to the first day of your next period. Unless you are tracking ovulation by a luteinising hormone test, a waking temperature record or serial progesterone measurements, you do not know yours — you are using the convention, which is 14 days and is the default here. The best available population figure is 12.4 days with a standard deviation of 2.4. A luteal phase shorter than about 10 days is commonly called a short luteal phase, though no single agreed threshold for it could be sourced for this page. The page will accept 9 to 18 days and will not tell you what any value means, because that is an interpretation rather than arithmetic.

Why does the window come out so wide?

Because its width is (your longest cycle − your shortest cycle) + 6 days, and that is the method being honest. The six is the measured fertile period — five days before ovulation plus the day itself. Everything on top of it is uncertainty about where ovulation lands, which comes from your own cycle variability, and the average woman’s cycle length moves by about 2.6 days from one cycle to the next even without unusual months. If you put your shortest and longest in as the same number you get the minimum six days, which looks reassuring and is not: it has not removed the uncertainty, only stopped displaying it.

What does the YYYYMMDD format mean?

It is ISO 8601 basic format: four digits of year, two of month, two of day, so 20260316 is 16 March 2026. The calculator underneath this page is a numeric expression evaluator with no date type at all — every date on it is a day number converted to and from a calendar by integer arithmetic — so a date has to come out as a number. The most important date, the day the window opens, is also printed as a separate year, month and day so there is nothing to misread.

Can a negative test before my period mean I am not pregnant?

Not reliably, and this is one of the better-documented limits in the subject. Implantation happens 6 to 12 days after ovulation, and in the cohort where that was measured about 10% of pregnancies were still undetectable by a highly sensitive test on the first day after the missed period, simply because implantation had been late and hCG had not risen yet. Waiting about a week past the expected period brings the false-negative rate down to 3% or less, which is why the test date this page prints is a week after the expected period rather than on it. The page cannot confirm or exclude a pregnancy and does not attempt to.

I have very irregular cycles, or no periods at all. Will this work?

It will produce numbers, and they will not be worth much. The method assumes your next cycle resembles your recent ones, and with irregular cycles that assumption is the whole of the error. The page will accept cycle lengths from 15 to 60 days and will flag a predicted ovulation earlier than day 8 or later than day 25, but flagging is all it can do — in the one study that estimated ovulation day directly, ovulation occurred as late as cycle day 60. Absent or very irregular periods are a reason to be assessed rather than to compute harder: cycle irregularity is one of the Rotterdam criteria, and thyroid and prolactin abnormalities both cause it.

Related calculators

References

Wilcox AJ, Dunson D, Baird DD. The timing of the “fertile window” in the menstrual cycle: day specific estimates from a prospective study. BMJ 2000;321(7271):1259–62. doi:10.1136/bmj.321.7271.1259. The source of every “what the calendar cannot see” figure on this page. 221 women contributing 696 cycles, with ovulation day estimated from daily urinary hormone measurement rather than assumed. Probability of being inside the fertile window: about 2% on cycle day 4, about 17% on day 7, peaking at about 54% on days 12 and 13, and at least 10% on every day from 6 to 21, with 4 to 6% of women still potentially fertile in the fifth week. Only about 30% of women had a fertile window falling entirely within days 10 to 17, and this held among women reporting regular cycles. Ovulation was observed as early as cycle day 8 and as late as day 60.
Wilcox AJ, Weinberg CR, Baird DD. Timing of sexual intercourse in relation to ovulation: effects on the probability of conception, survival of the pregnancy, and sex of the baby. N Engl J Med 1995;333(23):1517–21. The width of the window. 221 women, 625 cycles in which ovulation could be identified; conception occurred only when intercourse took place during a six-day period ending on the estimated day of ovulation. Day-specific probability of conception rose from about 0.10 five days before ovulation to about 0.33 on the day of ovulation. Important qualification, and the reason this page does not simply assert “five days before to one day after”: the authors state they cannot exclude a probability of conception of up to 0.12 on the seventh day before ovulation or on the day after it, with the confidence interval running from zero. The day after ovulation is therefore not excluded rather than demonstrated, and the six-day window is what was observed. The commonly quoted sperm survival of up to five days in the reproductive tract is an inference from this window rather than an independent measurement, and is presented that way here.
Centers for Disease Control and Prevention. Appendix D: Contraceptive Effectiveness, in U.S. Selected Practice Recommendations for Contraceptive Use, 2013. MMWR Recomm Rep 2014;63(4):47. The typical-use failure figure quoted in this page’s own prose and in the result card: fertility awareness-based methods, 24.0% of women experiencing an unintended pregnancy within the first year of typical use, with 47% still using the method at one year. Perfect-use figures in the same table are far lower and method-specific — 5.0% for the standard days method, 0.4% for the symptothermal method — which is exactly the gap this page exists to make visible. CDC states the table is adapted from Trussell J, Contraceptive efficacy, in Hatcher RA et al., Contraceptive Technology, 20th revised edition, Ardent Media, 2011. The underlying book is copyrighted; a CDC publication is a US Government work, and a single published percentage is a figure rather than an expression, so it is cited from CDC with the original attribution shown.
Peragallo Urrutia R, Polis CB, Jensen ET, Greene ME, Kennedy E, Stanford JB. Effectiveness of fertility awareness-based methods for pregnancy prevention: a systematic review. Obstet Gynecol 2018;132(3):591–604. The honest spread behind the single CDC number, and the reason this page quotes a range as well. 53 studies reviewed; study quality graded as 0 high, 21 moderate and 32 low. Typical-use first-year pregnancy rates from the moderate-quality studies ran from 10 to 33 per 100 users across the 12 of 14 methods with usable data, with the Sensiplan and Marquette monitor protocols at the better end (1.8 to 6.8) and most perfect-use figures between 1 and 5 per 100.
Bull JR, Rowland SP, Berglund Scherwitzl E, Scherwitzl R, Gemzell Danielsson K, Harper J. Real-world menstrual cycle characteristics of more than 600,000 menstrual cycles. npj Digital Medicine 2019;2:83. doi:10.1038/s41746-019-0152-7. Published CC BY 4.0, which permits commercial use with attribution. 612,613 ovulatory cycles from 124,648 users aged 18 to 45. Mean cycle length 29.3 days (SD 5.2); mean follicular phase 16.9 days (SD 5.3); mean luteal phase 12.4 days (SD 2.4); mean within-woman variation in cycle length 2.6 days (SD 2.5). Mean follicular phase length by cycle class: 10.4 days for cycles of 15 to 20 days, 15.2 days for 25 to 30, 26.8 days for 36 to 50. This is the quantitative basis for counting backwards from the next period rather than forwards from the last, and for the statement that the conventional 14-day luteal phase is about a day and a half longer than the measured mean.
Wilcox AJ, Baird DD, Dunson D, McChesney R, Weinberg CR. Natural limits of pregnancy testing in relation to the expected menstrual period. JAMA 2001;286(14):1759–61. The test-date figures. Even with a highly sensitive assay, about 10% of pregnancies are not detectable on the first day after the expected period, because implantation can be late; waiting about one week beyond the expected period reduces false negatives to 3% or less. This is why the date printed above is the expected period plus seven days rather than the expected period itself.
Wilcox AJ, Baird DD, Weinberg CR. Time of implantation of the conceptus and loss of pregnancy. N Engl J Med 1999;340(23):1796–9. The implantation range printed above: implantation occurred 6 to 12 days after ovulation. The National Institute of Environmental Health Sciences, which ran the Early Pregnancy Study, summarises the same finding as implantation occurring six to twelve days after conception, and the fertile window as the five days before ovulation plus the day of ovulation — a US Government summary of the same cohort. The median of about 9 days used for the middle row above is the figure the group’s own 2001 pregnancy-testing paper gives. Verification caveat: the authors, journal and year of this reference were confirmed against an independent listing, but the volume and page numbers are taken from the standard citation and were not re-verified against the primary text.
Ogino K. Published 1923 in the Hokuetsu Medical Journal. The calendar rule reproduced above as a comparison: the first fertile day is the shortest recent cycle minus 18 and the last is the longest minus 11, in cycle days. Ogino’s contribution was to count backwards from the next menstruation rather than forwards from the last, which is the same reasoning this page uses, supported in his case by histological examination of the ovaries of 65 women with very consistent cycles. Hermann Knaus reached minus 17 and minus 13 independently, presented at Leipzig in 1929. Dates and rule as recorded by the Museum of Contraception and Abortion, Vienna. A 1923 arithmetic rule is long out of copyright. The reading that Ogino’s 18 and 11 contain a fixed 14-day luteal phase plus four days before and three days after is this page’s arithmetic observation about the numbers, not a claim about Ogino’s stated reasoning.
American College of Obstetricians and Gynecologists, American Institute of Ultrasound in Medicine and Society for Maternal-Fetal Medicine. Methods for Estimating the Due Date. Committee Opinion No. 700. Obstet Gynecol 2017;129(5):e150–e154. Cited by number for two figures only: the estimated due date is 280 days after the first day of the last menstrual period, and an in vitro fertilisation pregnancy dated from a day-5 transfer is due 261 days later. Those two together fix conception at 14 days of gestational age, which is the identity that makes the due date printed on this page — ovulation plus 266 days — agree with the due date page exactly.
Verification note. The window arithmetic was swept rather than sampled. For every start date across a ten-year span, every cycle length from 20 to 45 days and every luteal phase from 9 to 17 days — 854,568 combinations — three identities were checked and held without exception: that the next expected period falls exactly the luteal-phase number of days after the predicted ovulation, that the predicted ovulation’s cycle day equals cycle length minus luteal phase plus one, and that each of the seven days from five before ovulation to one after round-trips through a calendar date and back to the same offset. The cross-check against the due date page — ovulation plus 266 days against that page’s cycle-adjusted 280-day rule — held for every one of those combinations with a 14-day luteal phase. The Gregorian-to-day-number conversion and its inverse were verified against an independent calendar implementation for all 73,414 dates from 1900 to 2100.

CalcEngines health calculators are for education and for checking arithmetic that has already been decided elsewhere. They are not medical advice, they do not decide what to give, and they do not replace the judgement of a doctor, nurse, midwife or dietitian who knows the person in front of them. Every figure depends on the values you enter and on the assumptions stated on the page — check it against the prescription, the product label and your local policy before acting on it.