Race Finish Time Predictor

Target pace {{ resultsReady ? formatPace(computation.values.pace_seconds_per_km, '/km') : '—' }} Adjustment {{ resultsReady ? formatSignedPercent(computation.normalizedInputs.adjust_percent) : '—' }}

Known race distance:

Choose the distance attached to the known finish time.

Known finish time:

Use MM:SS or H:MM:SS, for example 25:00.

Target race distance:

The model is most useful when the known and target races reflect similar fitness and conditions.

Endurance exponent:

Keep 1.06 unless you have evidence for a different personal distance profile.

Race-day adjustment:

The neutral default is 0%; this is a planning assumption, not part of the published Riegel equation.

Checkpoint unit:

This display preference does not reinterpret either race distance.

Prediction plan

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Calculation method:

Every visible result and handoff uses the same canonical computation.

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The chart renderer is unavailable. The same scenario values remain in the prediction plan.

Checkpoint	Distance	Elapsed	Average pace	Copy
{{ row.label }}	{{ row.distance }}	{{ row.elapsed }}	{{ row.pace }}

A recent race can anchor a pacing estimate for another distance. The useful question is not how long the new course would take at exactly the old pace, because runners generally slow as distance increases. A race-time model adds that endurance cost to the distance change.

The Riegel model expresses the relationship as a power law. Known time is multiplied by the target-to-known distance ratio raised to an endurance exponent. The widely used exponent 1.06 represents modest pace decay as distance grows; a higher exponent predicts more slowdown over a longer target and a lower exponent predicts less.

Factors that affect race-time projection quality
Factor	A closer match improves the estimate	A mismatch can distort it
Current fitness	Both races reflect the same training period	An old result may understate or overstate current ability
Effort	The known result was close to a full race effort	A training run builds its reserve into the prediction
Distance	Known and target events demand similar endurance	Large jumps depend heavily on the exponent
Conditions	Course, weather, altitude, and surface are comparable	Heat, hills, wind, or trail terrain can add substantial time

An exponent is a model choice, not a personal measurement unless it has been fitted from several representative results. Keeping 1.06 makes a neutral first estimate. Changing it can be useful when repeated races show a consistent personal distance profile, but adjusting it to force one desired answer hides uncertainty rather than reducing it.

Race-day adjustments belong outside the published power law. A positive percentage can model slower conditions and a negative percentage can model a faster course or unusually favorable conditions. The percentage is a planning assumption applied after the distance projection; it is not evidence that the conditions will change performance by exactly that amount.

Even checkpoint splits are another assumption. They divide the predicted finish time in proportion to distance and help build a pacing reference, but many courses and race plans call for uneven effort. Hills, congestion, aid stops, fatigue, and deliberate negative splitting can all produce sensible checkpoints that differ from an even ledger.

A predicted finish is an estimate, not a guarantee or a training prescription. Use recent workouts, course knowledge, health, recovery, and race-day judgment alongside the model.

How to Use This Tool:

Start with a recent, measured race completed near full effort and choose a target that reflects similar fitness.

Select the Known race distance and enter its Known finish time as MM:SS or H:MM:SS. Values such as 25:99 are rejected because clock seconds must stay below 60.
Choose the Target race distance. The main prediction and average target pace update when all three basic inputs are valid.
Open Advanced only when you have a reason to change the 1.06 Endurance exponent or add a Race-day adjustment. Positive adjustment makes the estimate slower; negative adjustment makes it faster.
Choose kilometers or miles for the Checkpoint unit, then compare Finish prediction, Condition sensitivity, and Checkpoint ledger. The unit changes checkpoint display, not the modeled race distances.

Interpreting Results:

Predicted finish includes both the distance-power estimate and the selected race-day adjustment. Before race-day adjustment isolates the published distance relationship, which makes it the better value for comparing exponent choices.

Average pace per km and Average pace per mile describe the same predicted speed in different units. They are finish-time averages, not instructions to hold identical effort on every hill, turn, or aid-station segment.

Condition sensitivity shows the selected adjustment with scenarios five percentage points faster and slower, bounded by the supported -15% to +30% range. That spread shows how strongly the assumption moves the finish; it is not a probability interval.

Confidence falls when the target is much longer than the known race, especially when projecting to a marathon from a short result. Check the prediction against recent long runs, a closer-distance race, and the actual course before setting a pacing target.

Technical Details:

The model keeps distance in metres and duration in seconds. Visible race choices run from 400 m through 50 km. Known time accepts 1 second through 7 days, the endurance exponent accepts 0.90 through 1.20, and race-day adjustment accepts -15% through +30%.

Formula Core

The baseline is the Riegel distance-power projection. The explicit condition multiplier is applied afterward.

\begin{matrix} T_{base} & = & T_{1} {(\frac{D_{2}}{D_{1}})}^{k} \\ T_{2} & = & T_{base} \times (1 + \frac{a}{100}) \end{matrix}

T₁ is the known finish in seconds, D₁ is its distance in metres, D₂ is target distance, k is the endurance exponent, and a is the race-day adjustment in percent. Equal source and target distances preserve the known time before adjustment.

Average pace divides the adjusted finish by target distance. The same physical pace is reported in both supported units.

\begin{matrix} p_{km} & = & \frac{T_{2}}{D_{2} / 1000} \\ p_{mi} & = & \frac{T_{2}}{D_{2} / 1609.344} \end{matrix}

Calculations retain full floating-point precision. Finish times, paces, and checkpoint times are rounded to the nearest whole second for display. Checkpoint elapsed time is 25%, 50%, 75%, or 100% of the adjusted prediction, which is why the ledger represents even average pacing.

Rule Core

Race prediction rules and boundaries
Rule	Exact behavior
Time syntax	`MM:SS` or `H:MM:SS`; seconds and three-part minutes must be 00 to 59.
Adjustment	Applied after the distance-power result; +5% multiplies baseline time by 1.05.
Sensitivity	Selected adjustment minus and plus 5 percentage points, clipped at -15% and +30%.
Checkpoint unit	Changes distance and pace display only; it does not convert or reinterpret the chosen event distances.

Accuracy Notes:

The original relationship was derived from athletic records, not from one runner's physiology, training load, fueling, injury history, or course. A later study of recreational runners found the common Riegel model reasonably calibrated through the half marathon in its sample but often too optimistic for marathon prediction.

Prefer a recent race close to the target distance over a much shorter effort.
Treat the race-day percentage as a scenario you chose, not measured uncertainty.
Do not use a projected pace to override pain, illness, unsafe weather, or professional medical advice.

Worked Examples:

A 25-minute 5 km projected to 10 km

Using 25:00 for 5 km, a 10 km target, exponent 1.06, and 0% adjustment gives 3,127.4 seconds before display rounding, shown as 52:07. The average pace is about 5:13 per km or 8:23 per mile. The -5% and +5% sensitivity scenarios display about 49:31 and 54:44. Those values are planning comparisons; they do not account for the runner's course or long-distance preparation.

References:

Athletic records and human endurance, P. S. Riegel, American Scientist, May–June 1981.
An empirical study of race times in recreational endurance runners, BMC Sports Science, Medicine and Rehabilitation, 2016.