The Runner's Math: Pace, Race Times and Heart-Rate Zones Explained

Almost all of running math comes down to three formulas. One turns a time and a distance into a pace. One turns a single race result into a prediction for every other distance. And one turns your age into the heart-rate zones you should train in. Learn these three and you can plan a training run, set a realistic race goal and structure your effort — all from a stopwatch.

1. Pace: time ÷ distance

Pace is how long it takes you to cover one unit of distance — minutes per kilometre or per mile. It’s just your time divided by the distance:

50:00 ÷ 10 km = 5:00 per km (about 8:03 per mile, or 12 km/h).

The real power is running it backwards to find a goal pace. Want a sub-4-hour marathon? Divide 4:00:00 by 42.195 km and you get 5:41 per km (9:09 per mile) — the pace you’d need to hold for all 42 km. Now you have a concrete number to practise in training. The running pace calculator does this in both directions, and the pace converter switches between min/km, min/mile and treadmill speeds.

2. Race prediction: the Riegel formula

How fast could you run a 10K based on your 5K? Peter Riegel’s endurance formula answers exactly that:

t₂ = t₁ × (d₂ ÷ d₁)^1.06

Your predicted time (t₂) for a new distance (d₂) equals your known time (t₁) over the known distance (d₁), scaled by the distance ratio raised to the power 1.06. That exponent — slightly greater than 1 — captures a basic truth: you can’t hold your 5K pace over a marathon, so pace slows as distance grows.

Take a 25:00 5K. Riegel predicts:

Distance	Predicted time
10K	~52:07
Half marathon	~1:55:00
Marathon	~3:59:47

So a 25-minute 5K runner has roughly four-hour-marathon potential. The big caveat: predictions assume you’ve done the training for the target distance. A marathon predicted from a 5K is only realistic if you’ve built the endurance with long runs — otherwise the real time is slower. The race time predictor builds this whole table from one result.

3. Heart-rate zones: training at the right intensity

Running the right effort matters as much as the right pace, and heart rate is how you measure effort. First estimate your maximum heart rate. The old rule is 220 − age, but the Tanaka formula is more accurate:

HRmax ≈ 208 − 0.7 × age → for a 30-year-old, about 187 bpm.

Then your training zones are percentage bands of that maximum:

Zone	% of max HR	Feels like	Purpose
1	50–60%	Very easy	Warm-up, recovery
2	60–70%	Conversational	Fat burn, aerobic base
3	70–80%	Comfortably hard	Aerobic, stamina
4	80–90%	Hard	Anaerobic threshold
5	90–100%	Maximal	VO₂ max, sprints

The counterintuitive part for many runners: most of your running should be easy (Zone 1–2), with only a small share of hard Zone 4–5 work. Piling on moderate-hard efforts every day is the classic mistake. If you enter your resting heart rate, the heart-rate zone calculator switches to the Karvonen method — target = (max − rest) × intensity + rest — which personalises the bands to your own heart-rate reserve.

Putting it together

These three tools work as a system: use the race predictor to set a realistic goal time, the pace calculator to turn that into a training pace, and the heart-rate zones to run your easy days genuinely easy so you’re fresh for the hard ones. Add the VO2 max calculator to track your aerobic fitness over time, and you can see progress in numbers — all computed privately in your browser.

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These are established exercise-science formulas — Riegel for prediction, Tanaka and Karvonen for heart rate — each an estimate calibrated on populations, not a personal guarantee. This is general fitness information, not medical advice; check with a doctor before hard training or a maximal test if you have any health concerns. Sources: Riegel P., “Athletic Records and Human Endurance” (American Scientist); Tanaka H. et al., J Am Coll Cardiol 2001; Karvonen M. et al. (heart-rate reserve).