Calculation Method
Distance constants, cumulative-time formulas, rounding rules and the limits behind PaceRibbon results.
Explicit distance constants
| Distance | Internal millimetres | Kilometres |
|---|---|---|
| 1 kilometre | 1,000,000 | 1 |
| 1 mile | 1,609,344 | 1.609344 |
| Half marathon | 21,097,500 | 21.0975 |
| Marathon | 42,195,000 | 42.195 |
Entered total durations use whole milliseconds. Named distances use the constants above. Custom decimal distances are converted using their selected unit, then rounded to the nearest millimetre. Display formatting is separate from calculation.
Cumulative times come from the original target
For an even plan, cumulative time = target time × marker distance ÷ full distance. The final marker uses the original target directly. The table does not repeatedly add a rounded pace. A two-half allocation applies its chosen first-half time before halfway and the remaining time after halfway.
Round once for reading
Non-negative display values use floor(value + 0.5) at the required precision. Cumulative and segment labels are rounded independently, so displayed subtraction or addition can differ by one second. CSV preserves raw distance and cumulative-time values for further arithmetic.
Output and input limits
| Item | Limit |
|---|---|
| Total distance | 100 m–100 km |
| Total duration | 1 second–48 hours |
| Unique split markers | 240 |
| Comparison plans | 2–4 for the same distance |
| Finish-time grid rows | 60 |
| First-half time share | 45%–55% |
| Lap length | 50–1,000 m |
| Local saved plans | 20 |
What is outside the model
The tools do not model fitness, injury, calories, incline, weather, terrain, GPS traces or the placement of course markers. They do not predict a finish at another distance from a previous result. Every output is a mathematical consequence of explicit inputs.