Throwing Sector and Circle Geometry Calculator
Throwing Sector and Circle Geometry Calculator
The sector angle from the two figures the IAAF facilities manual actually publishes — a length and a spacing — with the circle diameters beside it. The famous 34.92 degrees is not a chosen number: it is 2 × arcsin(0.3), the angle whose chord is six tenths of its radius, and the sector was 40 degrees until 2004.
Sector angle from a length and a spacing
2 × arcsin(chord ÷ 2r)The discus sector as the IAAF manual specifies it: 80 m long, lines 48 m apart, with the 2.50 m discus circle
Formula
sector angle = 2 × half-angle
sector area = ½ × length² × sector angle in radians
ring width = (2.50 − diameter) ÷ 2
- why arcsin and not arctan
- the manual specifies a CHORD — the straight spacing between the two lines at a given radius — and a chord of length c at radius R subtends 2 × arcsin(c / 2R). Using arctan(c / 2R) instead treats the spacing as measured along a perpendicular at the end of the centre line, and gives 33.398 degrees for the discus: plausible, close, and wrong
- radians, not degrees
- this engine’s trigonometry is in radians. deg() converts out and rad() converts in, and the sector area uses the radian value: half of 80² times 0.609385 radians is 1,950.0 m². A sector area computed with 34.9152 in place of the radians would be out by a factor of about 57
- 34.92 degrees
- IAAF Track and Field Facilities Manual, 2008 edition, in three separate sections: 2.4.1.4 for the discus, “Its angle of 34.92 degrees will be attained if the two sector lines at a distance of 80m are spaced 48m apart”; 2.4.2.4 for the hammer at 90 m and 54 m; and 2.4.4.4 for the shot at 25.00 m and 15 m. The exact value of 2 × arcsin(0.3) is 34.9152 degrees
- the javelin is not 34.92
- its sector is 50.00 m at 100 m, a ratio of 0.5 rather than 0.6, which is 2 × arcsin(0.25) = 28.9550 degrees — the figure usually quoted as 29. The manual states NO angle for the javelin at all: section 2.4.3.4 gives only “The length of the sector shall be 100m. At this distance the inner edges of the sector lines shall be 50.00m apart”, so the 28.9550 here is this page’s arithmetic on the manual’s own figures and not a quoted number
- 0.1825 m
- the manual’s own figure, in section 2.4.2.2, for the ring that reduces a 2.50 m discus circle to the 2.135 m hammer circle: “a 0.1825m wide and 0.02m high ring of suitable construction”. (2.50 − 2.135) ÷ 2 is 0.1825 exactly, which is the arithmetic check that both circle diameters were read correctly
Worked example
The discus sector as the IAAF manual specifies it: 80 m long, lines 48 m apart, with the 2.50 m discus circle
48 ÷ (2 × 80) = 0.3, so the half-angle is arcsin(0.3) = 17.4576 degrees
Twice that is 34.9152 degrees, which the manual prints as 34.92 in three separate sections
The spacing divided by the length is 0.6 exactly, and that ratio is the whole specification: the shot's 15 m at 25 m and the hammer's 54 m at 90 m are both 0.6 and both give 34.9152
In radians the sector is 0.609385, so the area out to 80 m is ½ × 80² × 0.609385 = 1,950.0 m²
Double both inputs to 160 m and 96 m and the angle does not move at all, because only the ratio matters
Transpose them — 48 m long, lines 80 m apart — and the answer becomes 112.885 degrees: a plausible-looking number from a transposition, which is why the page asks for the two separately
At the default 2.50 m the ring row is suppressed, because there is nothing to reduce; enter 2.135 instead and it reads 0.1825 m, the width the manual itself prints for the ring that turns a discus circle into a hammer circle
Enter the javelin's 100 m and 50.00 m and the angle is 28.9550 degrees, the figure usually quoted as 29 and one the manual never states
Every published sector, and the angle its figures imply
| Event | Sector length | Line spacing at that length | Spacing ÷ length | Angle, degrees | Angle the manual states |
|---|---|---|---|---|---|
| Shot put | 25.00 m | 15.00 m | 0.6000 | 34.9152 | 34.92 degrees |
| Discus | 80.00 m | 48.00 m | 0.6000 | 34.9152 | 34.92 degrees |
| Hammer | 90.00 m | 54.00 m | 0.6000 | 34.9152 | 34.92 degrees |
| Javelin | 100.00 m | 50.00 m | 0.5000 | 28.9550 | none stated |
The circles, the rim and the stop board
| Item | Published figure | Section | Check |
|---|---|---|---|
| Shot put circle, inside diameter | 2.135 m ± 0.005 m | 2.4.4.2 | circumference 6.7073 m |
| Hammer circle, inside diameter | 2.135 m ± 0.005 m | 2.4.2.2 | the same circle as the shot |
| Discus circle, inside diameter | 2.50 m ± 0.005 m | 2.1.1.3 | circumference 7.8540 m |
| Ring reducing a discus circle to a hammer circle | 0.1825 m wide, 0.02 m high | 2.4.2.2 | (2.50 − 2.135) ÷ 2 = 0.1825 exactly |
| Circle rim | at least 6 mm thick, 70 mm to 80 mm deep, white | 2.4.1.2 | interior 0.02 m ± 0.006 m below the rim |
| Shot put stop board | 1.21 m ± 0.01 m long, 0.112 m ± 0.002 m at its narrowest, 0.10 m ± 0.002 m high | 2.1.1.3 and 2.4.4.3 | no equivalent for discus or hammer |
| Javelin throwing arc | 0.07 m wide, white, radius 8.00 m | 2.4.3.3 | the only curved release line in the field events |
| Sector lines | 0.05 m wide, inside edges form the boundary | 2.4.1.4 | so a mark on the line is in |
The angle was 40 degrees, and that is a dated change
| What | Figure | Source | Status |
|---|---|---|---|
| Current sector, shot, discus and hammer | 34.92 degrees | IAAF Track and Field Facilities Manual, 2008 edition | first-party, quoted |
| Exact value of the construction | 34.9152 degrees | 2 × arcsin(0.3), from the manual’s own length and spacing | this page’s arithmetic |
| Previous sector | 40 degrees | Wikipedia, Shot put: narrowed “most recently in 2004 from 40°” | secondary, not a governing body |
| Year of the change | 2004 | the same article | secondary; no World Athletics statement found |
A ratio of six tenths, printed as an angle
This page is about athletics — track and field, and road running — whose competition rules, technical rules and scoring tables are published by World Athletics, the body that was the IAAF until 2019. Where a figure below belongs to a particular edition of those rules, the edition is named beside it, because World Athletics revises them and a number quoted without its edition will be wrong for somebody.
The sector angle is a derived figure, which is why it is 34.92 degrees and not 35. The IAAF Track and Field Facilities Manual never asks anybody to set out an angle: it gives a length and a spacing, and says the angle “will be attained if the two sector lines at a distance of 80m are spaced 48m apart”. Forty-eight over eighty is 0.6, and so is fifteen over twenty-five for the shot and fifty-four over ninety for the hammer. An angle whose chord is six tenths of its radius is 2 × arcsin(0.3), which is 34.9152 degrees, and the manual prints that rounded to 34.92. The figure is therefore a consequence of a ratio a pair of officials can lay out with a tape — ten metres out from the centre of the circle, six metres across — rather than a number anybody chose.
So the page asks for the manual’s two figures rather than for an angle: it reproduces the specification instead of paraphrasing it, and a transposition then shows up at once. Forty-eight metres at eighty gives 34.9152 degrees; eighty metres at forty-eight gives 112.885, which looks like a number and is not an answer.
The javelin is the exception and it is instructive. Its sector is 50.00 m at 100 m — a ratio of 0.5, not 0.6 — which works out at 28.9550 degrees, the figure usually quoted as 29. The manual states no angle for it whatsoever: section 2.4.3.4 gives only the length and the spacing, and adds that the sector lines are “laid from the centre point on the runway through the crosspoints of the throwing arc”, because a javelin is thrown from behind an arc of 8.00 m radius rather than from a circle. So the 28.9550 on this page is derived from the manual’s figures and is labelled as derived, not quoted.
The circles are specified separately from the sectors and nothing connects them arithmetically. The shot put and the hammer share a circle of 2.135 m plus or minus 0.005 m; the discus has 2.50 m. The evidence that those two diameters were read correctly is a third published figure depending on both: the manual reduces a discus circle to a hammer circle “by inserting a 0.1825m wide and 0.02m high ring”, and (2.50 − 2.135) ÷ 2 is 0.1825 exactly — two numbers from different sections agreeing through a third, which is worth more than reading either of them twice when a document’s drawings do not come through.
One detail decides arguments on a Saturday afternoon. The sector lines are 0.05 m wide and, in the manual’s words, “the inside edges of which form the boundary of the sector”. The paint is therefore outside the sector: an implement landing on the line is a valid throw, because the line itself is not in. The same convention runs through the rest of the specification — the circle diameter is measured inside the rim, and the javelin’s sector spacing is between the inner edges of its lines.
An honest note about which edition this is. World Athletics publishes the Competition Rules and the Technical Rules as one combined PDF, and the three copies of it that returned readable text at all — the current official one, last modified 1 July 2026; a member federation’s copy of the edition in force from 1 November 2019; and a school board’s copy of the edition effective 1 January 2022 — return between 100,000 and 123,000 characters each and then stop. The current one stops inside the Technical Rules at about Rule 5, and a fourth copy, an official asset file, returned no readable text whatever. So the rule text quoted here was read in an earlier edition, and where a figure could also be found in World Athletics Council’s own March 2025 amendment table it is taken from there instead, because that table prints the current and the amended wording side by side. Check a rule number against the edition your competition is run under.
And the change of angle, which is the kind of thing this plugin exists to print with a date beside it, is where the sourcing runs out. The sector used to be wider: Wikipedia’s shot put article records that it “has been narrowed multiple times over the years to improve safety, most recently in 2004 from 40°”, and its hammer throw article gives the same reason for the odd figure that the manual’s own arithmetic implies — “easy to measure and lay out on a field (10 metres out from the center of the ring, 6 metres across)”. Neither is a governing body, and no World Athletics or IAAF statement of the change or its date was found: the current Technical Rules stop at about Rule 5 in every copy fetched, and the Council’s March 2025 amendment table has no throwing entry. So the 2004 date is on this page as a secondary attribution and is marked as one. A 40 degree sector is 2 × arcsin of 0.342, a ratio of 0.684 rather than 0.6, so the old construction was not a round ratio either.
For the other exactly published geometry in this category, the track lane distance and stagger calculator works a 400 m track to the millimetre, and the hurdle spacing and flights interpreter has the hurdle table. For what a throw is worth once it is measured, the combined events scoring calculator has the published closed form, including the detail that a throw goes into it in metres while a jump goes in as centimetres.
Frequently asked questions
What is the throwing sector angle?
34.92 degrees for the shot put, the discus and the hammer, as the IAAF Track and Field Facilities Manual states in three separate sections. The exact value of the construction it describes is 34.9152 degrees. The javelin is narrower at about 28.96 degrees, and the manual states no angle for it at all.
Was the sector always 34.92 degrees?
No. It was 40 degrees before 2004, according to Wikipedia’s shot put article, which says the sector “has been narrowed multiple times over the years to improve safety, most recently in 2004 from 40°”. That is a secondary source: no World Athletics or IAAF statement of the change or its date was found for this page, and the page says so rather than implying otherwise.
How big are the throwing circles?
2.135 m plus or minus 0.005 m inside the rim for the shot put and the hammer, and 2.50 m for the discus. A discus circle is converted to a hammer circle with “a 0.1825m wide and 0.02m high ring”, which is exactly half the difference between the two diameters.
Is a throw landing on the sector line in or out?
In. The lines are 0.05 m wide and the manual says “the inside edges of which form the boundary of the sector”, so the painted line lies outside the sector and an implement touching it has landed inside.
Why does the calculator want a length and a spacing instead of an angle?
Because that is what the specification is, and because two independent inputs catch a mistake an angle would hide. Transposing them — 48 m long with lines 80 m apart — gives 112.885 degrees rather than 34.9152, which is obviously wrong; a single angle field would have no such check. It also means the page works for a school sector laid out to any length, since only the ratio decides the angle.
Related calculators
References
- IAAF. Requirements for Planning, Constructing, Equipping and Maintaining IAAF Track and Field Facilities Manual, 2008 Edition, “Copyright by: IAAF – 2008”, Editions EGC, ISBN 2-911469-37-2. Read 15 Oct 2026 from the copy hosted by mastershistory.org; 113,664 characters of readable text covering Chapters 1 and 2 and truncating inside Chapter 2, with every figure below coming through as TEXT while the numbered figures and drawings are absent — which matters, because this manual’s dimensions mostly live in drawings. Section 2.1.1.3 summarises the four facilities: discus, circle “2.50m ± 0.005m diameter” and sector “80m radius, 48m chord”; hammer, “2.135m ± 0.005m”, protective cage, “90m radius, 54m chord”; javelin, “runway (30m min. x 4m), arc with a radius of 8m and landing sector (100m radius, 50.00m chord)”; shot put, “2.135m ± 0.005m”, stop board “1.21m ± 0.01m x 0.112m x 0.10m ± 0.02m”, sector “25m radius, 15m chord”. The sector angle is stated in three sections in one form of words, quoted here from 2.4.1.4 (discus): “The landing sector must be laid from the middle of the circle with an angle of 34.92 degrees”, marked “by 0.05m wide white lines, the inside edges of which form the boundary of the sector”, and “Its angle of 34.92 degrees will be attained if the two sector lines at a distance of 80m are spaced 48m apart”. 2.4.2.4 repeats it for the hammer at 90m and 54m and 2.4.4.4 for the shot at 25.00m and 15m. Also: 2.4.4.2 and 2.4.2.2, the shot and hammer circle “2.135m ± 0.005m”, a discus circle reduced to it “by inserting a 0.1825m wide and 0.02m high ring of suitable construction”; 2.4.4.3, the stop board “0.112m ± 0.002m” wide and “0.10m ± 0.002m” high; 2.4.1.2, the rim “at least 6mm thick, 70mm to 80mm deep and painted white” with the interior “0.02m ± 0.006m lower”; 2.4.3.3, the javelin arc “0.07m wide, white and curved with a radius of 8.00m”; 2.4.3.4, its sector lines “laid from the centre point on the runway through the crosspoints of the throwing arc”, “100m” long with “the inner edges of the sector lines … 50.00m apart”. NOTE WHAT IS ABSENT: no angle is stated for the javelin sector, and no earlier sector angle is stated anywhere.
- Wikipedia. Shot put (read 15 Oct 2026; about 70,000 characters including tables and references). Cited for two things the IAAF manual does not say. First, the historical angle: the sector “has been narrowed multiple times over the years to improve safety, most recently in 2004 from 40°”, with no date beyond the year. Second, the reason for the odd figure: the 34.92° angle “was chosen because it provides a sector whose bounds are easy to measure”. It gives the current sector as “a circular sector of 34.92° centered on the throwing circle” and the circle as “2.135 metres (7 ft) in diameter”. NOT a governing body, and no World Athletics or IAAF statement of the change or its date was found — the current Technical Rules could not be read past Rule 5 and the Council’s March 2025 amendment table carries no throwing entry.
- Wikipedia. Hammer throw (read 15 Oct 2026; about 30,000 characters in total, roughly 6,000 of prose). An independent statement of the same two facts: “The hammer must land within a 34.92º throwing sector that is centered on the throwing circle”, and the angle “was chosen because it provides a sector whose bounds are easy to measure and lay out on a field (10 metres out from the center of the ring, 6 metres across)” — which is the 0.6 ratio this page’s arithmetic turns on, stated in metres. It gives no earlier sector angle and no change date. Not a governing body.
- World Athletics. Book C — C1.1 & C2.1: Competition Rules & Technical Rules, the single combined PDF linked from worldathletics.org/about-iaaf/documents/book-of-rules, listed there as last modified 1 July 2026 (fetched 15 Oct 2026). CITED FOR WHAT IT COULD NOT DELIVER, because that is load-bearing: the fetch returns 123,065 characters of readable text and stops inside the Technical Rules at about Rule 5, so Technical Rules 19, 22, 23, 24 and 32 to 34 are NOT in the readable text of the current edition. Its amendment table came through, with effective dates running from 17 December 2020 to 1 July 2026. The page lists C1.1 and C2.1 as one document, so there is no shorter Technical Rules file to fetch instead.
- World Athletics Council. Competition and Technical Rule Amendments approved by World Athletics Council — March 2025, read 15 Oct 2026 from the copy published by the Bulgarian Athletics Federation (bfla.eu); about 10,000 characters, the amendment table readable as text. Cited here only for an absence that is load-bearing: the table prints current and amended wording side by side for Technical Rules 22 and 24 among others, and carries NO entry for Technical Rule 23 or for Technical Rules 32 to 34, so it offers nothing on the steeplechase or on the throwing events. It is quoted in full on the pages where it does supply a figure.