Power-law race time scenario
Mistake: Treating the example exponent as a guaranteed prediction.
Fix: Choose an exponent appropriate to your scenario and treat the result as a model, not a race promise.
Calculators · Free
Power-law race time scenario
Project another race distance with a user-chosen endurance exponent.
01Enter your values
Runs in your browserRuns offline in your browser. Once the page and required files have loaded, processing needs no internet.
02Power-law race time scenario
Runs in your browser
How it works
Project another race distance with a user-chosen endurance exponent.
T₂ = T₁ × (D₂/D₁)ᵏ
A power-law scenario, not a validated personal performance forecast. The exponent is user-supplied; 1.06 is an example, not a universal constant. Training, terrain, weather, fatigue and fueling are not modeled. Works offline after loading.
Your data stays yours
Inputs are processed on this page and are never sent to a server.
About this tool
Use tool ↑Project another race distance with a user-chosen endurance exponent.
T₂ = T₁ × (D₂ / D₁)^k. Enter a completed race time and distance, a target distance and an exponent. Convert both distances using the same unit system before calculating.
How to use it
- Enter your values
Known race distance · Known race time · Target race distance · Endurance exponent
- Calculate / generate
Project another race distance with a user-chosen endurance exponent.
- Result
Projected minutes: 52.123288 min Distance ratio: 2
Calculation method
- T₂ = T₁ × (D₂ / D₁)^k.
- Enter a completed race time and distance, a target distance and an exponent.
- Convert both distances using the same unit system before calculating.
T₂ = T₁ × (D₂/D₁)ᵏ
Power-law race time scenario
- Known race distance
- 5 km
- Known race time
- 25 min
- Target race distance
- 10 km
- Endurance exponent
- 1.06
Result
Projected minutes: 52.123288 min Distance ratio: 2
Frequently asked questions
What does this result assume?
A power-law scenario, not a validated personal performance forecast. The exponent is user-supplied; 1.06 is an example, not a universal constant. Training, terrain, weather, fatigue and fueling are not modeled. Works offline after loading.
Where does my data go?
Calculations run on your device. Form inputs are not sent to a server.
Terms and definitions
Enter your values
- Measurement system
The initial choice follows your browser region. Your choice is remembered on this device. Gallons are US gallons. Switching units keeps your numbers unchanged and interprets them in the new unit.
Numbers stay unchanged. Check the new unit and enter the intended measurement, or select an example for that system.
- Known race distance
Distance corresponding to the supplied completed race time.
Enter a numerical value for this quantity. Use the unit shown beside this field. km / mi
Minimum: 1e-9 · Maximum: 1000000000000 km
- Known race time
Elapsed time of the known race, in minutes.
Enter a numerical value for this quantity. Use the unit shown beside this field. min
Minimum: 1e-9 · Maximum: 1000000000000 min
- Target race distance
Positive distance to project.
Enter a numerical value for this quantity. Use the unit shown beside this field. km / mi
Minimum: 1e-9 · Maximum: 1000000000000 km
- Endurance exponent
User-chosen power-law exponent; it controls how time scales with distance.
Enter a numerical value for this quantity.
Minimum: 0 · Maximum: 10
Result
- Result
T₂ = T₁ × (D₂ / D₁)^k. Enter a completed race time and distance, a target distance and an exponent. Convert both distances using the same unit system before calculating.
Calculated from your entries using the method below.
- Projected minutes
Known time multiplied by the distance ratio raised to the selected exponent.
Calculated from your entries using the method below.
- Distance ratio
Target distance divided by known distance.
Calculated from your entries using the method below.
- Value
T₂ = T₁ × (D₂ / D₁)^k. Enter a completed race time and distance, a target distance and an exponent. Convert both distances using the same unit system before calculating.
Calculated from your entries using the method below.
- Unit
Convert both distances using the same unit system before calculating.
Calculated from your entries using the method below.
Common mistakes and quick fixes
Limits and key assumptions
- A power-law scenario, not a validated personal performance forecast. The exponent is user-supplied; 1.06 is an example, not a universal constant. Training, terrain, weather, fatigue and fueling are not modeled. Works offline after loading.
- Displayed results may be rounded; rounding does not add measurement precision.