Course Measurement Calculator

What this page does

A course measurement calculator answers one narrow question. Your finish time was run over a course that is not exactly the nominal distance, so what would the same pace have produced over the exact distance. Enter the distance, the time, and how far the course was off — a certificate, a re-measurement or a race director's announcement will give you that third number — and the page returns the time on the exact distance, the seconds the difference is worth, the error in metres per kilometre, and what one part per thousand costs over that distance.

No other page on this site takes a course's error as an input. The race time calculator prices a course's elevation profile, the marathon split calculator splits a target time over a profile you type, and the race pace calculator converts between pace, time and distance. This page moves one time between two lengths at one fixed pace, which is a different question: not what the hills cost, but what the tape said.

Everything runs in your browser. Nothing you type is sent to a server, there is no account and no upload, and the numbers never leave the page. The arithmetic is two divisions; the rules behind the numbers in the prose are quoted with their sources below.

How the numbers are calculated

Three things go in: the nominal distance D₀ in metres, the finish time T in seconds, and the course error e in metres, signed. The length you actually covered is D = D₀ + e, and the pace you held is that time divided by that length:

p = T ÷ D    T₀ = p × D₀

T₀ is the number in the big slot: the time the same pace would have produced over the exact distance. The difference the page prints is T₀ − T, so a short course gives a positive number — the seconds you would have given back on a full-length course — and a long course gives a negative one. Every other number on the page is the same p used once more: pace per kilometre is 1000p, pace per mile is 1609.344p, the error per kilometre is 1000e ÷ D₀, and 100 m of course is 100p seconds.

Nothing here is a model. There is no coefficient, no correction factor and no fitted curve: the whole page is one division and one multiplication, run on the numbers you supply. That is deliberate, because a course's error is a length, and a length converts into a time exactly once you fix the pace.

• D₀ — the nominal distance in metres: 5,000 for 5K, 10,000 for 10K, 21,097.5 for a half marathon, 42,195 for a marathon.
• T — your finish time in seconds, as hh:mm:ss or mm:ss.
• e — the course error in metres, negative when the course is short and positive when it is long.
• p — the pace you held, in seconds per metre. Multiply by 1000 for the pace per kilometre.
• 1 mile = 1609.344 m exactly — the international mile, fixed by the 1959 yard and pound agreement. A definition, not a measurement.

A worked example: a marathon in 3:30:00 on a course 100 m short

The course was 42,095 m, not 42,195 m. The pace is 12,600 ÷ 42,095 = 0.299323 s/m, which is 4:59.3 per kilometre and 8:02.4 per mile. Over the exact 42,195 m that pace is 0.299323 × 42,195 = 12,629.9 s, printed 3:30:30 — so the 100 m is worth 29.9 s. The error is 100 ÷ 42.195 = 2.37 m per kilometre, which is 2.4 times the one-part-per-thousand factor, and one part per thousand over this distance is 42.195 × 0.299323 = 12.6 s.

The reverse block runs the same division backwards. 30 s at that pace is 30 ÷ 0.299323 = 100.2 m of course, or 2.38 m per kilometre. A time that is 30 s faster than you expected and a course that is 100 m short are the same size of thing, which is exactly why the two are so easy to confuse.

The tolerance in the rules, and what it is worth to you

Road courses are not measured to a target with a tolerance either side of it. USA Track and Field states the rule plainly on its course-certification pages: measurement along the Shortest Possible Route and use of a one-part-per-thousand Short Course Prevention Factor are hard-wired into the rules, so they apply whatever method a measurer uses. One part per thousand is 1 m per kilometre, and over the four standard distances it is worth this much:

• 5K — 5 m of course, which at 5:00 per kilometre is 1.5 s.
• 10K — 10 m, which at 5:00 per kilometre is 3.0 s.
• Half marathon — 21.1 m, which at 5:00 per kilometre is 6.3 s.
• Marathon — 42.195 m, which at 5:00 per kilometre is 12.7 s.

The direction matters more than the size. Doug Thurston, a World Athletics and AIMS Level A measurer, writes that a certified course can be slightly long but it cannot be short, and describes courses he measured 50 or so feet long because moving the start or the finish was not practical. The name of the factor says the same thing: it is a short course prevention factor. The error the rules guard against is the one that makes times look fast, so the built-in bias points the other way — a certified course is more likely to hand you a few seconds than to take them.

Two dates belong to this section, because they are the part of a certificate that expires. World Athletics requires a valid International Course Measurement Certificate established no more than five years before the date of the race for a performance to count for its top lists, entry standards or records. A USA Track and Field certification runs for ten years, and the higher-profile events affiliated with World Athletics, AIMS or the Abbott World Marathon Majors are re-measured every five. A course number that is older than the rule for the event you are looking at is a fact about the paperwork, not about the road.

What this page cannot do is tell you the error for a specific race. It has no certificate database and no race list, and it will not guess a length for a course it has not been given. Type the number, and it does the arithmetic.

What 100 m of course is worth at your pace

The seconds in 100 m depend on your pace and on nothing else — not the distance, not the race, not the surface. 100 m is one tenth of a kilometre, so at x seconds per kilometre it is x ÷ 10 seconds:

• 4:00 per km — 100 m is 24 s.
• 5:00 per km — 100 m is 30 s.
• 6:00 per km — 100 m is 36 s.
• 7:00 per km — 100 m is 42 s.

That is why the same 100 m matters so differently by distance. It is 2% of a 5K and 0.24% of a marathon, but the seconds it hands back are set by how fast you are running, so a 100 m error is worth twice as much time to a 4:00 runner as to an 8:00 runner over any distance at all. Two worked cases with the same pace in them: a 5K run in 25:00 over a 4,900 m course is 5:06.1 per kilometre, and that pace over a full 5,000 m is 25:31. A marathon run in 3:30:00 over 42,095 m is 4:59.3 per kilometre, and over 42,195 m it is 3:30:30.

Keep the sign straight when you use these numbers on a real result. A course that came out short takes seconds off your time and gives them back when you correct to the full distance; a course that came out long adds seconds you did not earn, and correcting to the nominal distance takes them away. The table above prints both directions around your own figure, from 200 m short to 200 m long, so the sign is visible rather than remembered.

How a road course is actually measured

Not with a satellite receiver and not with a map drawn on a website. The method the rules were written around, described by Thurston for Running USA, is a bicycle fitted with a calibrated mechanical counter on the front wheel:

• Calibrate first. The measurer rides a calibration course that has been measured with a steel tape or a laser, usually 1,000 feet or 300 metres, and reads the counter before and after each measuring session.
• Convert counts to metres. From the calibration ride the measurer works out how many counter counts make a kilometre, a mile and the whole race distance.
• Ride the line the runners will have. On race day, at race-day setup, cutting every tangent — that is what the Shortest Possible Route means. Where a parked car or a locked gate blocks the line, the measurer offsets around it and keeps the arithmetic straight.
• Place the marks from that ride. The start, the finish and the intermediate marks are set from the measured line, not from a map.
• Submit. The map, the data, the start and finish elevations and the separation between them go to a certifier, who issues the certificate number.

Two consequences follow, and both are the reason this page exists. The measured line is the shortest line a runner can legally take, so a runner who does not cut every tangent covers slightly more than the measured distance — the course is right and the runner is long. And the number on the certificate describes the line the measurer rode, not the position of the signs on the morning; a mark set a few metres out is a race-day placement question, and the certificate cannot answer it.

If you are measuring a loop of your own, the honest description of a watch is that it estimates and a calibrated counter measures. The rules do not accept GPS for certification, and the next section says why the two disagree by so much.

When the kilometre mark and your watch disagree

In the ordinary case, the mark is right and the watch is long, and the size of the gap is known. Thurston's figure, from years of measuring with a receiver on the handlebars as a cross-check, is that GPS devices almost always over-estimate the race distance by at least one percent, or about 50 feet per mile. One percent of a half marathon is 211 m, which at 5:00 per kilometre is 63 s; one percent of a marathon is 422 m, or 127 s at the same pace. That is not a rounding difference, it is a minute and more of clock.

Part of that is the receiver and part of it is you. A watch samples a wandering line rather than a taut one, and most runners do not run the shortest line either — every water stop, every crowded corner and every overtake adds a little. The measured course is the shortest line; the watch records the line you actually took. So a watch reading 13.25 miles for a half marathon is not evidence that the course is long, it is evidence that a GPS track is not a measurement.

What to do with a disagreement, then. If the gap grows with every kilometre — two hundred metres at 10 km, four hundred at 20 km — it is a percentage, and a percentage is the watch. If a single mark is out by a few metres and the next one is back on the number, that is a sign placed in the wrong spot on the day, which is a race-organisation question and not a measurement one. Neither case is a reason to change the arithmetic on this page, which takes the course error as a number you supply rather than a number it can detect.

Supported range and limits

• Distance: 400 to 100,000 m. Below 400 m the course error is a large fraction of the distance and the correction stops being meaningful; above 100 km it is no longer a road race this page is built for.
• Time: 1:00 to 23:59:59, as hh:mm:ss or mm:ss.
• Course error: −1,000 to +1,000 m, and the resulting course length must stay positive. That covers every certificate error and every race-director announcement you are likely to meet; a course 1 km out over a marathon is already 2.4% and well outside anything the rules would certify.
• Rounding: times to the nearest second, paces to a tenth of a second, metres to one decimal. One rounding, at the end, never halfway through a chain.
• Cost: none. No account, no email, no paywall, no daily limit, no request to a server.
• Privacy: every number is computed in your browser. Nothing you type is sent anywhere or stored — reload the page and it is gone.
• Works offline once the page has loaded, and on a phone.

What this page deliberately does not do

• No course database and no race presets. There is no option that loads a named race, because a preset would mean shipping a length for a real course, and courses are re-measured. The same choice is made on the marathon split calculator and the marathon pace band, for the same reason.
• No GPS file upload and no track analysis. This page does not read a .gpx or a .fit file and cannot measure your line. It takes a course error as a number.
• No elevation, weather or wind correction. A climb, a headwind and a hot day all change the cost of a distance, and none of them is a course-length error. The race time calculator and the marathon split calculator price elevation with a published energy-cost model; this page prices length only.
• No prediction. It converts a time you already ran between two lengths. Telling you what you are capable of is the race time predictor on the home page, which moves a recent result along the distance curve.
• No certification service and no claim about any race. It cannot look up a certificate number, and it does not say whether a course is certified, when it was measured or who measured it.
• No judgement on whether a time counts. The five-year and ten-year rules are quoted above because they are facts about certificates. Applying them to a result, or deciding whether a performance is record-eligible, is not something this page does.

Questions

What does a course measurement calculator do?

It moves a finish time from the course you ran to the exact nominal distance, at the pace you held. Enter the distance, the time and how far the course was off, and it prints the time on the exact distance, the seconds the difference is worth, the error in metres per kilometre and the pace you actually ran. Nothing is predicted: the pace is your own result divided by the length you covered, and the only other number involved is the length the race was supposed to be.

How many seconds is 100 m on a race course?

It depends only on your pace, not on the distance. 100 m is one tenth of a kilometre, so at 5:00 per kilometre it is 30 s, at 4:00 it is 24 s, at 6:00 it is 36 s and at 7:00 it is 42 s. A 5K run in 25:00 over a course measured 100 m short is 5:06.1 per kilometre, and that pace over a full 5,000 m is 25:31. A marathon run in 3:30:00 over 42,095 m is 4:59.3 per kilometre, and over 42,195 m it is 3:30:30.

What is the short course prevention factor?

One part per thousand, which is 1 m per kilometre. USA Track and Field states that measurement along the shortest possible route and the one-part-per-thousand short course prevention factor are hard-wired into its rules, so they apply whatever method a measurer uses. Over a marathon the factor is 42.195 m of course, worth 12.7 s at 5:00 per kilometre; over a 5K it is 5 m, worth 1.5 s at the same pace.

Can a certified course be long?

Yes, and it may not be short. Doug Thurston, a World Athletics and AIMS Level A measurer, writes that a certified course can be slightly long but it cannot be short, and describes courses that came out 50 or so feet long because moving the start or the finish was not practical. The rule points the same way: the factor is a short course prevention factor, so the error it guards against is the one that makes times look fast rather than the one that makes them look slow.

My watch says the course was long. Which is right?

The marks, in the ordinary case. GPS is not used to measure or certify a course, and Thurston's figure is that watches over-estimate race distance by at least one percent, or about 50 feet per mile, because the receiver wanders and because most runners do not run the shortest line. One percent of a half marathon is 211 m, which at 5:00 per kilometre is 63 s. A gap that grows with every kilometre is a percentage and belongs to the watch; a single mark a few metres out is a placement question on the day.

How is a road course measured?

With a bicycle carrying a calibrated mechanical counter on the front wheel. The measurer calibrates on a course measured with a steel tape or a laser, usually 1,000 feet or 300 metres, before and after each session, converts counts into metres, then rides the line the runners will have on race day, cutting every tangent. The ride, the map and the start and finish elevations go to a certifier, who issues the certificate number.

How long does a course certificate last?

World Athletics requires a valid International Course Measurement Certificate established no more than five years before the date of the race for a performance to count for its top lists, entry standards or records. A USA Track and Field certification runs for ten years, and the higher-profile events affiliated with World Athletics, AIMS or the Abbott World Marathon Majors are re-measured every five. An older number is a fact about the paperwork rather than about the road.

Does this page tell me whether a race is certified?

No. It has no certificate database and no race list, and it cannot look up a course number. It takes the error you type and does the arithmetic with it. The certificate is issued by a certifier and published by the federation, so the entry list or the race website is where the number for a specific race lives.