Pace & Speed Converter

Start from:

Use pace for a watch or race target; use speed for a treadmill or GPS average.

Running pace:

Decimal minutes are converted to a clock pace in the result; changing units preserves the same physical speed.

Running speed:

The converter calculates pace from the selected speed without applying grade, wind, terrain, or fatigue adjustments.

Reference distance:

The 5 km default makes timing and projection artifacts immediately useful; changing units preserves the same physical distance.

Projection profile:

Balanced uses 1.06; endurance-leaning uses 1.04; speed-leaning uses 1.08.

Split spacing:

The default 1 km multiplier is neutral for the calculation and creates familiar course checkpoints.

Custom goal distance:

Use 0 to omit the custom projection; changing units preserves the same physical distance.

Extra numeric decimals:

The default 0 is neutral and keeps standard two-decimal numeric displays.

Measure	Metric	Imperial	Basis	Copy
Correct the active pace or speed input to restore the conversion.
{{ row.label }}	{{ row.metric }}	{{ row.imperial }}	{{ row.basis }}

Conversion logic

Pace to speed: speed = 60 ÷ pace in minutes per unit
Speed to pace: pace = 60 ÷ speed per hour
Unit bridge: One international mile is exactly 1.609344 kilometres.
Reference time: Elapsed time is canonical seconds per kilometre multiplied by the reference distance in kilometres.
Split checkpoints: Each cumulative checkpoint uses the same steady pace; the final checkpoint is always the exact reference distance.
Race projection: T₂ = T₁ × (D₂ ÷ D₁)^R, where the selected Riegel exponent R is 1.04, 1.06, or 1.08.

Conversion and checkpoints are deterministic. Race projections are directional estimates and do not model training status, treadmill grade, elevation, wind, surface, acceleration, fatigue, GPS error, or race-course tolerances.

A treadmill may show kilometres per hour while a training plan gives minutes per mile. Both describe the same motion from opposite directions: speed is distance covered per unit of time, and pace is time needed per unit of distance. A faster speed therefore produces a smaller pace number.

The distinction matters when moving among watches, treadmills, race plans, and course markers. A pace of 5:00 min/km is exactly 12 km/h on level ground. Converting the same physical speed to imperial units gives about 8:03 min/mi and 7.46 mph; the runner has not become faster or slower because the unit changed.

Pace, speed, and finish-time distinctions
Measure	Typical form	Useful for
Pace	min/km or min/mi	Watch targets, splits, and race plans
Speed	km/h, mph, or m/s	Treadmills, GPS averages, and motion comparisons
Finish time	hh:mm:ss	A fixed distance at unchanged pace
Race projection	Projected clock time	A different distance with a fatigue adjustment

A steady-pace finish time is arithmetic, not a prediction: it assumes the same ground speed from start to finish. A race projection makes a stronger assumption. The Riegel power model adjusts time as distance changes, but its exponent can only approximate how endurance, training, terrain, weather, elevation, and race execution affect a particular runner.

Use a recent sustained effort over a distance that resembles the target when projecting a race. A short sprint is a poor basis for a marathon, and a hilly trail effort is not directly comparable with a flat road course. Even a well-chosen reference gives a planning range rather than a guaranteed finish.

How to Use This Tool:

Choose the measurement you already know; switching between pace and speed preserves the same physical speed.

Select Pace or Speed, enter the value, and choose kilometres or miles. Pace accepts decimal minutes, so 5.5 means 5 minutes 30 seconds.
Enter a Reference distance to calculate its steady finish time, then set Split spacing for cumulative checkpoints. Increase the spacing if the result would exceed 100 checkpoints.
Choose a Projection profile. Balanced uses exponent 1.06, endurance-leaning uses 1.04, and speed-leaning uses 1.08.
Add a nonzero Custom goal distance only when a standard 5K, 10K, 10-mile, half-marathon, or marathon projection is not enough.
Compare Current equivalence with the reference finish and projection rows. Use extra numeric decimals for conversion detail; clock values still round to the nearest second.

Interpreting Results:

The metric and imperial pace and speed values are exact unit equivalents before display rounding. Reference finish and split checkpoints assume unchanged pace. Projection rows use the selected exponent, so they should not be read as another unit conversion.

A lower exponent produces a faster long-distance projection from the same reference effort; a higher exponent adds more slowdown as distance grows. Compare projected times only when the reference effort, course type, and profile stay consistent.

Technical Details:

Pace and speed are reciprocals once their time and distance units are aligned. The calculation uses seconds per kilometre as its central quantity, converts one international mile as exactly 1.609344 kilometres, and derives every displayed unit from that same value.

Formula Core:

For speed in kilometres per hour, dividing 3,600 seconds by speed gives seconds per kilometre. Pace entered per mile is divided by 1.609344 to obtain the equivalent seconds per kilometre.

\begin{matrix} p_{km} & = & \frac{3600}{v_{kmh}} \\ p_{mi} & = & p_{km} \times 1.609344 \\ v_{mph} & = & \frac{v_{kmh}}{1.609344} \\ T & = & D \times p_{km} \end{matrix}

p is pace in seconds per distance unit, v is speed, D is distance in kilometres, and T is elapsed seconds. Split times apply the final equation to each cumulative checkpoint, always including the finish even when the chosen spacing does not divide the course evenly.

Race projections use the reference time and the ratio between target and reference distances. The exponent controls how strongly the predicted time departs from linear scaling.

T_{2} = T_{1} \times {(\frac{D_{2}}{D_{1}})}^{b}

Race projection profile exponents
Profile	Exponent b	Longer-distance effect
Endurance-leaning	1.04	Least modeled slowdown
Balanced	1.06	Middle estimate
Speed-leaning	1.08	Most modeled slowdown

Inputs accept pace from 0.1 through 120 decimal minutes per selected unit, speed from 0.1 through 200, and distances from 0.01 through 1,000 in the selected unit. Numeric conversion values retain full precision; pace and clock strings round to the nearest second.

Limitations:

The conversion is deterministic, but finish and race projections simplify running conditions.

Steady calculations do not adjust for grade, wind, heat, altitude, surfaces, stops, acceleration, or fatigue.
Riegel profiles are general power-law scenarios, not a fitted personal model.
GPS distance error, treadmill calibration, and course measurement can be larger than the displayed decimal precision.
Very different reference and target distances usually produce less reliable projections.

Worked Examples:

Five-minute kilometre pace

A pace of 5.00 min/km equals 12.00 km/h and produces a 25:00 steady 5K finish with checkpoints at 5:00 intervals. Using that 25:00 effort as the reference, the balanced 1.06 profile projects about 52:07 for 10K and about 3:59:47 for a marathon. The first time is direct multiplication; the longer predictions include the selected fatigue exponent.

References:

Athletic records and human endurance, Peter S. Riegel, American Scientist, 1981.
The International System of Units, National Institute of Standards and Technology.