Mean Arterial Pressure (MAP) Calculator
Mean Arterial Pressure (MAP) Calculator
MAP by the one-third rule and by the two published heart-rate-corrected forms, which disagree by several mmHg at a fast rate — because the one-third rule assumes a cardiac cycle that a tachycardic patient does not have.
Mean arterial pressure, three published forms
DBP + f × pulse pressureSBP 124 mmHg, DBP 72 mmHg, heart rate 96, one-third rule
Why there are three formulas and none of them is the mean
One-third rule: f = 1/3, so MAP = DBP + (SBP − DBP)/3 = (SBP + 2×DBP)/3
Razminia 2004: f = 1/3 + 0.0012 × HR
Moran 1995: f = 0.01 × e^(4.14 − 40.74/HR)
- the true mean
- the time integral of the arterial pressure waveform over one cardiac cycle, divided by the cycle length. An arterial line’s monitor computes it; two cuff numbers cannot, because they say nothing about the shape of the curve between them
- why 1/3
- the rule assumes diastole occupies two thirds of the cardiac cycle and systole one third, so a third of the pulse pressure is added to the diastolic. The equivalent algebraic form (SBP + 2×DBP)/3, which the Edwards reference card prints, is the same statement
- why it fails at speed
- diastole shortens far more than systole as heart rate rises, so systole takes a larger fraction of the cycle and the mean moves up towards the systolic. The one-third rule, which has no rate term, therefore underestimates the mean in a tachycardic patient, and the size of the error is a fraction of the pulse pressure
- Razminia’s form
- f = 1/3 + 0.0012 × HR. At 60 beats per minute that is 0.405, at 100 it is 0.453 — never the bare third, even at a slow rate
- Moran’s form
- f = 0.01 × e^(4.14 − 40.74/HR), derived across exercise heart rates. At 60 it gives 0.319, at 100 it gives 0.418. It crosses the one-third line at about 65 beats per minute, where Razminia’s never does — so the two published corrections disagree with each other as well as with the rule
- how big is the error
- one comparison of the standard formula against the alternatives found its error was not random but patterned: the deviation correlated negatively with pulse pressure (R = −0.561) and positively with heart rate (R = 0.298). In other words it is systematic, and it is worst in exactly the tachycardic, wide-pulse-pressure patient in whom a mean pressure is most often being chased
- MAP is not perfusion pressure
- the pressure driving flow through an organ is the mean arterial pressure minus the pressure downstream of it. Subtract the central venous pressure for most beds; in abdominal compartment syndrome subtract the intra-abdominal pressure instead, because that is what the renal vein is squeezed by. A mean of 75 with a CVP of 20 is a perfusion pressure of 55
Worked example
SBP 124 mmHg, DBP 72 mmHg, heart rate 96, one-third rule
Pulse pressure = 124 − 72 = 52 mmHg
One-third rule: 72 + 52 ÷ 3 = 72 + 17.33 = 89.3 mmHg. Equivalently (124 + 2 × 72) ÷ 3 = 89.3
Razminia's form factor at 96 beats per minute: 1/3 + 0.0012 × 96 = 0.4485, so 72 + 0.4485 × 52 = 95.3 mmHg
Moran's form factor at 96: 0.01 × e^(4.14 − 0.4244) = 0.4108, so 72 + 0.4108 × 52 = 93.4 mmHg
The three published forms span 6.0 mmHg on the same patient, and the one-third rule is the lowest of them — the direction the physiology predicts at a rate of 96
Slow the same patient to 60 and the three become 89.3, 93.1 and 88.6. Moran's now sits BELOW the one-third rule, so the two corrections disagree about the direction of the correction at a slow rate
Take the same form factors to a rate of 150 and the spread widens to 98.7 and 96.9 against the rule's unchanged 89.3
Now the perfusion-pressure point. This mean of 89.3 with a central venous pressure of 4 is a perfusion pressure of 85.3. With a CVP of 20 it is 69.3 — the same mean arterial pressure and nearly a fifth less driving pressure across the kidney
The three form factors across the heart rate range
| Heart rate | One-third rule | Razminia 2004 | Moran 1995 |
|---|---|---|---|
| 40 | 0.333 | 0.381 | 0.227 |
| 60 | 0.333 | 0.405 | 0.318 |
| 80 | 0.333 | 0.429 | 0.377 |
| 100 | 0.333 | 0.453 | 0.418 |
| 120 | 0.333 | 0.477 | 0.447 |
| 150 | 0.333 | 0.513 | 0.479 |
| 180 | 0.333 | 0.549 | 0.501 |
Mean arterial pressure, and what it is not
| Figure | What it is | Source or caveat |
|---|---|---|
| MAP, published range | 70 to 105 mmHg | Edwards Lifesciences reference card, which prints the formula as (SBP + 2 × DBP)/3 |
| Perfusion pressure | MAP − CVP for most organ beds | Not a published range. At a CVP of 20 a MAP of 75 gives 55 |
| Abdominal perfusion pressure | MAP − intra-abdominal pressure, where that is raised | The renal vein is compressed by the abdominal pressure, not by the CVP |
| The true mean | The time integral of the pressure waveform over the cycle | Only an arterial line gives it. Nothing computed from two cuff numbers is this |
The one-third rule is a low-heart-rate approximation
The true mean arterial pressure is the area under the arterial pressure curve for one cardiac cycle divided by the length of that cycle. An arterial line’s monitor computes exactly that, by integration, and if you have one its number is better than anything on this page. What a cuff gives instead is two points on the curve, a peak and a trough, and every formula for mean arterial pressure from a cuff is a guess at the shape of the curve between them.
The familiar guess is that diastole takes two thirds of the cycle and systole one third, which gives the mean as the diastolic plus a third of the pulse pressure — or equivalently, as the reference cards print it, the systolic plus twice the diastolic all over three. That assumption is approximately true at a resting rate of around sixty and progressively false above it, because diastole shortens far more than systole as the rate rises. A tachycardic patient spends a larger fraction of each cycle in systole, the true mean moves up towards the systolic, and a formula with no heart rate term reads low.
Two published corrections add the rate term, and they do not agree with each other. Razminia and colleagues give the fraction as a third plus 0.0012 times the heart rate, which is 0.405 at sixty and 0.453 at a hundred — never the bare third, even slowly. Moran and colleagues, working across exercise heart rates, give it as 0.01 times e to the power of 4.14 minus 40.74 over the rate, which is 0.319 at sixty and 0.418 at a hundred, and so crosses the one-third line at around sixty-five. At a rate of ninety-six on a pulse pressure of fifty-two the three forms span six mmHg. One comparison of the standard formula against these alternatives found its error was systematic rather than random: it correlated negatively with pulse pressure and positively with heart rate, so it is worst in exactly the fast, wide-pulse-pressure patient whose mean pressure is being chased.
The larger point is that mean arterial pressure is not perfusion pressure. What drives flow through an organ is the mean arterial pressure minus whatever pressure sits downstream of it, and that subtraction is frequently the whole story. A mean of 75 with a central venous pressure of 4 leaves 71 mmHg; the same mean with a central venous pressure of 20 leaves 55. In abdominal compartment syndrome the relevant subtraction is the intra-abdominal pressure rather than the CVP, because that is what the renal vein is being squeezed by. A mean inside a published range can therefore sit on top of a perfusion pressure that is not. Every figure here is derived from other measurements, so it carries their errors as well as its own. A derived index is never more reliable than the least reliable number that went into it. A derived haemodynamic number is read alongside the patient — the history, the perfusion, the lactate, the trend across serial measurements — and never instead of them. It supports a clinician’s judgement rather than replacing it.
Frequently asked questions
What is the formula for mean arterial pressure?
The familiar one is diastolic pressure plus a third of the pulse pressure, which is the same as (systolic + 2 × diastolic) ÷ 3. At 124/72 that is 89.3 mmHg. Two published forms add a heart rate term instead: Razminia’s fraction is 1/3 + 0.0012 × HR and Moran’s is 0.01 × e^(4.14 − 40.74/HR). At a rate of 96 the same 124/72 gives 95.3 and 93.4 mmHg respectively.
Why does the one-third rule fail at a fast heart rate?
Because the third is a statement about the cardiac cycle, not about pressure: the rule assumes diastole occupies two thirds of the cycle. As heart rate rises diastole shortens disproportionately, systole takes a larger share, and the true mean moves up towards the systolic. A formula with no rate term therefore reads progressively low, and the size of the shortfall is a fraction of the pulse pressure — so it is worst in a fast patient with a wide pulse pressure.
Which mean arterial pressure formula should I use?
If there is an arterial line, use the monitor’s integrated mean rather than any formula, because it measures what the formulas approximate. From a cuff there is no settled answer: the one-third rule is universal and rate-blind, and the two published corrections disagree with each other as well as with it. This page prints all three on every calculation so the spread is visible, and says which one the headline figure used.
Is a normal mean arterial pressure the same as adequate perfusion?
No. Perfusion pressure is the mean arterial pressure minus the pressure downstream of the organ — usually the central venous pressure, or the intra-abdominal pressure where that is raised. A mean of 75 is 71 mmHg of driving pressure at a CVP of 4 and 55 mmHg at a CVP of 20. Published MAP ranges say nothing about that subtraction.
Can the mean arterial pressure be above the systolic?
Not by any of these formulas. Every form adds a positive fraction of the pulse pressure to the diastolic, and all three fractions are between 0 and 1, so the result always lies between the diastolic and the systolic and equals both when they are equal. A monitor reporting a mean outside that interval is reporting an artefact — a damped or whipped arterial trace, most often.
Related calculators
References
- Edwards Lifesciences. Normal Hemodynamic Parameters and Lab Values (EU master reference card). Cardiac output 4–8 L/min, cardiac index 2.5–4 L/min/m², stroke volume 60–100 mL/beat, stroke volume index 33–47 mL/m²/beat, SVR 800–1200 and SVRI 1970–2390 dyn·s·cm⁻⁵ (·m²), PVR 100–250 dyn·s·cm⁻⁵, MAP 70–105 mmHg, CVP 2–6 mmHg, PAWP 6–12 mmHg; prints MAP as “[SBP + (2 x DBP)]/3” and SVR as “MAP-RAP x 80/CO”.
- Razminia M, Trivedi A, Molnar J, et al. Validation of a new formula for mean arterial pressure calculation: the new formula is superior to the standard formula. Catheter Cardiovasc Interv. 2004;63(4):419–25. The form factor is heart-rate dependent: 1/3 + 0.0012 × HR, so the fraction of the pulse pressure added to the diastolic rises with rate rather than staying at a third.
- Moran D, Epstein Y, Keren G, Laor A, Sherez J, Shapiro Y. Calculation of mean arterial pressure during exercise as a function of heart rate. Appl Human Sci. 1995;14(6):293–5. Form factor 0.01 × e^(4.14 − 40.74/HR), derived across exercise heart rates.
- Nguyen H. The logarithmic relationship between mean arterial pressure and heart rate. arXiv:2503.23140. Reproduces the Moran and Razminia form factors side by side as “FS = 0.01e^(4.14−40.74/HR)” and “FS = 1/3 + 0.0012HR”, and notes that the one-third heuristic is recovered only as a special case near 60 beats per minute. The source the two coefficient sets on this page were read in; the Razminia paper itself was not reachable from here.
- The effect of heart rate and pulse pressure on mean arterial pressure: the combined formula. Mustafa Kemal University open access repository (item 25c5508d). Found the standard formula’s error is patterned rather than random: “PP coefficient deviation of the standard formula was negatively correlated with PP (R = -0,561, P < 0.001), and positively correlated with HR (R = 0,298, P = 0.003)”.
Not medical advice. For healthcare professionals and education. Reference intervals vary by laboratory and assay — always use your own laboratory's. Never base a dose or a treatment decision on this page alone. Full disclaimer at calcengines.com/disclaimer/