What is the Riegel formula?

The Riegel formula is a mathematical model that predicts race time at one distance based on performance at another. It uses the equation T₂ = T₁ × (D₂/D₁)^1.06, where the exponent 1.06 represents the fatigue effect as distance increases. Peter Riegel published this relationship in 1977 after analyzing race results across multiple distances.

Why is the exponent 1.06 instead of 1.0?

An exponent of 1.0 would imply that performance scales linearly with distance—that doubling distance exactly doubles time. The 1.06 exponent reflects empirical observation that endurance deteriorates slightly with longer distances. This means a runner who completes 5K in 20 minutes will typically take more than 40 minutes for 10K, because the body fatigues nonlinearly.

How accurate are these predictions?

Accuracy depends on how similar the known and target distances are, and whether conditions remain consistent. The formula tends to perform well within one step of common race distances (5K to 10K, 10K to half-marathon). Predictions become less reliable when extrapolating across very different distances or when training status, terrain, or weather conditions change significantly.

Can this formula predict marathon time from a 5K?

The calculator will generate a result, but large distance ratios reduce reliability. Predicting marathon performance from a 5K involves extrapolating across a 8.4× distance increase, where differences in aerobic capacity, fuel utilization, and training specificity become significant. More accurate marathon predictions typically use a half-marathon or other long-distance result as the baseline.

Does the calculator adjust for hills or weather?

No. The Riegel formula is purely mathematical and does not account for course elevation, temperature, humidity, wind, or surface conditions. The prediction assumes equivalent race environments. Adjustments for these factors require separate correction models or empirical data from similar courses.

Running

Race Time Predictor (Riegel Formula)

Estimate race finish time at a new distance using the Riegel formula and a known performance.

Last updated: 22 April 2026

What this tool does

This calculator estimates race finish time at a new distance using the Riegel formula, a widely used endurance prediction model published by Peter Riegel in 1977. It requires a known race distance and finish time, plus a target race distance, and applies the equation T₂ = T₁ × (D₂/D₁)^1.06 to predict performance at the new distance, outputting an estimated finish time and corresponding pace. The formula assumes similar training status and race conditions between performances and is most reliable for distances within the same general event category (e.g., 5K to half-marathon).

Inputs

Result

—

Formula Used

T_{2} = T_{1} \times (\frac{D _{2}}{D _{1}})^{1.06}

D_{1}

Known distance in km

T_{1}

Known time in minutes

D_{2}

Target distance in km

Spotted something off? Let us know — we update calculators regularly.

How Race Time Predictor (Riegel Formula) works

This calculator applies the Riegel formula to estimate race finish time for a target distance based on a known performance at a different distance. The tool takes a completed race result—your known distance and time—and projects what that performance translates to over a longer or shorter distance. The output is a predicted finish time for the target event, formatted in hours, minutes, and seconds, along with the equivalent pace per kilometer.

The formula

The Riegel formula is expressed as:

T₂ = T₁ × (D₂ / D₁)^1.06

Where:

T₁ = known race time (in minutes)
D₁ = known race distance (in kilometers)
T₂ = predicted race time (in minutes)
D₂ = target race distance (in kilometers)
1.06 = the fatigue exponent, representing the nonlinear relationship between distance and performance

The exponent of 1.06 reflects the observation that endurance performance deteriorates slightly as distance increases, rather than scaling linearly. This constant was derived from statistical analysis of race results across multiple distances.

Where this method is most accurate

The Riegel formula tends to perform best when the known and target distances are relatively close—typically within one order of magnitude (for example, predicting 10K from 5K, or half-marathon from 10K). Predictions become less reliable when extrapolating across very large distance ratios, such as estimating marathon time from an 800m result. The formula assumes consistent training, similar race conditions, and that the runner's aerobic profile remains stable between efforts. It does not account for differences in terrain, elevation, weather, or changes in fitness level over time.

What this tool does not do

This calculator generates a mathematical estimate based solely on the formula above. It does not provide training plans, pacing strategies, or personalized coaching. The tool does not assess individual health status, injury risk, or readiness for a particular distance. It cannot account for race-day variables such as heat, humidity, altitude, or course difficulty. The prediction is a statistical projection, not a guarantee of actual race performance. Users remain responsible for all training and racing decisions.

Disclaimer

This tool is for educational and informational purposes only. It is not medical, health, or training advice. The calculator provides estimates derived from a published formula; individual results may vary significantly. Consult qualified professionals—such as coaches, physicians, or certified trainers—before beginning or modifying any training program. No calculator can replace individualized assessment or professional guidance.

Questions

What is the Riegel formula?: The Riegel formula is a mathematical model that predicts race time at one distance based on performance at another. It uses the equation T₂ = T₁ × (D₂/D₁)^1.06, where the exponent 1.06 represents the fatigue effect as distance increases. Peter Riegel published this relationship in 1977 after analyzing race results across multiple distances.
Why is the exponent 1.06 instead of 1.0?: An exponent of 1.0 would imply that performance scales linearly with distance—that doubling distance exactly doubles time. The 1.06 exponent reflects empirical observation that endurance deteriorates slightly with longer distances. This means a runner who completes 5K in 20 minutes will typically take more than 40 minutes for 10K, because the body fatigues nonlinearly.
How accurate are these predictions?: Accuracy depends on how similar the known and target distances are, and whether conditions remain consistent. The formula tends to perform well within one step of common race distances (5K to 10K, 10K to half-marathon). Predictions become less reliable when extrapolating across very different distances or when training status, terrain, or weather conditions change significantly.
Can this formula predict marathon time from a 5K?: The calculator will generate a result, but large distance ratios reduce reliability. Predicting marathon performance from a 5K involves extrapolating across a 8.4× distance increase, where differences in aerobic capacity, fuel utilization, and training specificity become significant. More accurate marathon predictions typically use a half-marathon or other long-distance result as the baseline.
Does the calculator adjust for hills or weather?: No. The Riegel formula is purely mathematical and does not account for course elevation, temperature, humidity, wind, or surface conditions. The prediction assumes equivalent race environments. Adjustments for these factors require separate correction models or empirical data from similar courses.

Sources & Methodology

Applies the Riegel formula: T₂ = T₁ × (D₂/D₁)^1.06, where T₁ is known race time, D₁ is known distance, D₂ is target distance, and 1.06 is the empirically derived fatigue exponent. Originally published by Peter Riegel in Runner's World (1977).

More in Running

View all 15 →