About this tool
The Riegel formula predicts race times across distances based on a recent performance. A 45-minute 10K predicts a 1:39 half marathon and 3:28 marathon. The formula assumes you've trained appropriately for the target distance - it doesn't predict an untrained marathon from a 5K.
How it works
Enter a recent race distance and time. The calculator predicts your time at any other distance, plus quick-reference times at 5K, 10K, half, and full marathon.
Heart rate zones and training science
Max heart rate (HRmax) is the upper bound your cardiovascular system can sustain for short bursts. The simplest estimate is the Fox formula: HRmax = 220 - age. Better is the Tanaka formula: HRmax = 208 - 0.7 x age, which is more accurate for adults above 40. Both are population averages with ±10 bpm individual variance.
Training zones (% of HRmax)
| Zone | % HRmax | Effort | Use |
|---|---|---|---|
| 1 Recovery | 50-60% | Very easy chat pace | Active recovery between sessions |
| 2 Endurance | 60-70% | Conversational | Aerobic base; 70-80% of weekly volume should be here |
| 3 Tempo | 70-80% | Comfortably hard, short sentences | Lactate threshold work, 30-60 min |
| 4 Threshold | 80-90% | Hard, breathing labored | VO2 max intervals, 3-8 min reps |
| 5 Anaerobic | 90-100% | All out | Sprints, 20-90 seconds |
1RM strength formulas
One-rep max (1RM) is the maximum weight you can lift once. Multiple-rep estimates:
- Epley: 1RM = weight x (1 + reps / 30)
- Brzycki: 1RM = weight x 36 / (37 - reps) - more accurate for 1-10 reps
- Lander: 1RM = weight x 100 / (101.3 - 2.67123 x reps)
Reps above 12 lose accuracy across all formulas. For periodized training, use 5-rep max (5RM) as a working metric and recompute every 6-8 weeks.
Pace, distance, time triangle
Endurance training revolves around three numbers - any two give the third:
- Pace = Time / Distance
- Time = Pace x Distance
- Distance = Time / Pace
Common race times and required paces (km):
| Event | Sub-elite | Recreational | Beginner |
|---|---|---|---|
| 5K | 20:00 (4:00/km) | 30:00 (6:00/km) | 40:00 (8:00/km) |
| 10K | 42:00 (4:12/km) | 60:00 (6:00/km) | 80:00 (8:00/km) |
| Half marathon | 1:35 (4:30/km) | 2:15 (6:24/km) | 3:00 (8:32/km) |
| Marathon | 3:30 (4:58/km) | 4:30 (6:24/km) | 5:30 (7:49/km) |
VO2 max ranges (ml/kg/min)
| Age | Elite men/women | Average men/women | Sedentary men/women |
|---|---|---|---|
| 20s | 75 / 65 | 44 / 38 | <35 / <30 |
| 30s | 70 / 60 | 42 / 36 | <33 / <28 |
| 40s | 65 / 55 | 39 / 33 | <31 / <26 |
| 50s | 60 / 50 | 36 / 31 | <28 / <24 |
| 60s | 55 / 45 | 33 / 28 | <26 / <22 |
The formula explained
This calculator uses the following formula:
T2 = T1 × (D2/D1)^1.06 - Pete Riegel's 1981 formula. Accurate within 2-3 percent for trained runners.
The reason this formula works is rooted in the underlying physics, finance, or biology of the problem. Behind every calculator is a published, peer-reviewed equation or a widely accepted convention. We do not invent formulas; we apply standard ones from textbooks, government tables, professional bodies, and academic literature.
If you are curious about the math, the simplest way to verify is to plug in two known numbers and compare against a known result. The calculator should match published examples to within rounding precision.
Frequently asked questions
How accurate is Riegel?
Within 2-3 percent for similarly trained runners. Marathon predictions are less reliable if you haven't done long runs.
Why 1.06 exponent?
Riegel found this fit empirically. Lower exponents (1.00) assume same pace; higher (1.10+) penalize longer distances more.
Newer formulas?
Cameron's, Vickers, and others tweak the exponent for elite vs recreational. For most amateurs, Riegel is good enough.
Why does my marathon predict slower?
Marathon-specific endurance (>2 hours) requires different training. The formula assumes adequate long-run prep.
How accurate is the 220-age formula?
Within about ±10 bpm for most adults. For people over 40, the Tanaka formula (208 - 0.7 x age) is closer to actual lab-measured HRmax. The only way to know your true HRmax is a maximal effort test - sprint until exhaustion.
Should I train mostly hard or mostly easy?
Mostly easy. Elite endurance athletes spend 70-80% of training time in zones 1-2. The polarized model (mostly easy + a small dose of very hard) consistently beats the threshold-heavy approach for long-term improvement.
How often should I retest my 1RM?
Every 6-8 weeks at most. True 1RM attempts are stressful and require taper. Most periodized programs use 3-5RM as a working number and recompute 1RM via the Epley or Brzycki formula.
What is heart rate variability (HRV) and why does it matter?
HRV is the variation in time between heartbeats. Higher HRV indicates better recovery. Track it via Whoop, Oura, Garmin, or Polar. Drops of 10%+ from your baseline often signal under-recovery or illness onset.
How do I know if I'm overtraining?
Signs: elevated resting heart rate, drop in HRV, sleep disruption, persistent fatigue, plateau or regression in performance, increased injuries. Reduce volume 30-50% for 1-2 weeks and monitor.
How accurate is the Race Time Predictor?
It applies the standard formula. Accuracy is limited only by your input precision. For decisions with material consequences (taxes, medical, legal, structural), use the result as a starting point and verify with a qualified professional in the relevant field.
Is the Race Time Predictor free to use?
Yes. 100% free, no signup, no payment, no API key. The site is funded by display ads around the tool but not inside the calculation flow.
Are my inputs saved anywhere?
No. All inputs stay in your browser tab. Closing the tab discards them. The site uses Google Analytics for traffic measurement (anonymized) but the analytics never see what you type into the form.
Can I use the Race Time Predictor on my phone?
Yes. The tool is responsive and tested on iOS Safari, Android Chrome, and major desktop browsers. Touch targets meet Apple's 44pt and Google's 48dp minimum.
Does the Race Time Predictor work offline?
Yes. Once the page has loaded, it works without internet. The calculation runs in JavaScript on your device.
How do I report a bug or suggest improvement to the Race Time Predictor?
Email hi@3tej.com with the URL of this page and a description of what you saw vs expected. We typically respond within 72 hours.
Can I share results from the Race Time Predictor?
Take a screenshot or copy the output. The page doesn't generate shareable URLs for specific calculations - inputs stay in your browser only.
Why are the results different from another race time predictor tool?
Most likely: different formula assumptions, different default values, different rounding rules, or different applicable rates. Check the methodology if both tools document it. Both can be valid for different scenarios.