How Running Pace and Riegel Projections Work
A cautious walkthrough of min/km math and simple distance scaling—without promising race-day magic
How Running Pace and Riegel Projections Work
Runners often stare at a finish clock and wonder what it means for the next race. Pace worksheets turn distance and time into readable averages. Riegel projections add a second layer: simple endurance scaling to another distance.
This article explains the arithmetic: total seconds ÷ kilometers for pace, distance ÷ hours for speed, and optional T2 = T1 × (D2/D1)^exponent. It will not build a training plan, estimate VO2max, or model heat and hills.
The Question Pace Math Can Answer
A good worksheet answers: what average pace and speed does this finish imply? Projection asks what another distance might look like under a simple scaling law—not what your body guarantees on race day.
Practical pace habits
- Convert miles to kilometers before entry when needed
- Use a recent comparable effort for projections
- Start with recreational exponent 1.06 unless you have a reason not to
- Expect hills, heat, and fitness to change outcomes
- Treat coaching plans as separate from this math
Try the Running Pace Worksheet
Convert a finish into pace and optional Riegel projection:
Open Running Pace CalculatorA Transparent Worked Example
A 50-minute 10K is 5:00 /km and 12 km/h. Projecting to 21.0975 km with exponent 1.06 yields about 6619 seconds (roughly 1:50:19) and about 5:14 /km—an estimate only.
What moves pace and projection
| If you change… | Typical effect | Still does not prove… |
|---|---|---|
| Faster finish at same distance | Lower min/km and higher km/h | Fitness for a longer race |
| Larger target distance | Longer projected time under Riegel | A course-specific guarantee |
| Higher exponent | More time added as distance grows | That the exponent matches your physiology |
What the Model Leaves Out
Outside the educational scope
- VO2max lab testing
- Heat, altitude, and grade models
- Periodized coaching plans
- Guaranteed race outcomes
If you take one habit into pace worksheets, take this: make finish times readable, keep projections humble, and leave medical and coaching decisions to people—not to a scaling exponent.