About Race Time Predictor
Race Time Predictor: Riegel Formula for 5K, 10K, Half Marathon, and Marathon
TL;DR: Enter a recent race distance and finish time. The predictor applies the Riegel formula — T₂ = T₁ × (D₂/D₁)^1.06 — to project your finish time at the 5K, 10K, half marathon, and marathon distances. Understand accuracy limits, how to adjust for course and conditions, and how to use predictions to set training targets and race goals.
Table of Contents
- The Riegel Formula: How Race Time Prediction Works
- What the 1.06 Exponent Actually Means
- Accuracy: When to Trust the Prediction and When Not To
- Prediction Tables: 5K Through Marathon
- How to Use This Predictor (Step by Step)
- Six Worked Examples Across Distances and Ability Levels
- How to Adjust Predictions for Course and Conditions
- Using Predictions for Goal-Setting and Training Targets
- The Riegel Formula vs. Other Prediction Methods
- FAQ
- Assumptions and Notes
- Further Reading
The Riegel Formula: How Race Time Prediction Works
T₂ = T₁ × (D₂ / D₁)^1.06
Where:
- T₁ = your known finish time (in seconds)
- D₁ = your known race distance (in km)
- D₂ = the target distance you want to predict (in km)
- T₂ = predicted finish time (in seconds, convert to hh:mm:ss)
- 1.06 = the fatigue coefficient
Source: Riegel, P.S. (1981). Athletic records and human endurance. American Scientist, 69(3), 285–290. PMID: 7235349.
Example: Predicting a marathon from a 10K result
A runner finishes a 10K in 48:00 (2,880 seconds). Predicting the marathon (42.195 km):
T₂ = 2,880 × (42.195 / 10)^1.06
= 2,880 × (4.2195)^1.06
= 2,880 × 4.528
= 13,041 seconds
= 3:37:21
The formula has only two moving parts: the distance ratio (D₂/D₁) raised to the fatigue power (1.06). Everything else — pace, training volume, race conditions — is not in the formula. This simplicity is both its strength and its limitation.
What the 1.06 Exponent Actually Means
The exponent 1.06 is the number that makes race time prediction non-linear. Without it — if the exponent were 1.0 — the formula would produce pure linear scaling: doubling your distance would exactly double your time, meaning pace stays constant regardless of distance. But pace does not stay constant. Every runner slows down over longer distances, and 1.06 encodes how much.
The mathematics of pace degradation:
At an exponent of 1.0 (linear, no fatigue): running twice as far takes exactly twice as long. At an exponent of 1.06 (Riegel): running twice as far takes 2^1.06 = 2.083× as long — your average pace is 4.1% slower.
For a runner covering 4× the distance: 4^1.06 = 4.245× as long — pace is 6.1% slower.
This compounding is why marathon predictions from 5K times feel aggressive: the 5K-to-marathon ratio is 8.44×, so 8.44^1.06 = 9.14× — pace degrades by 8.3% across the distance span.
Why 1.06 specifically? Riegel analysed world record performances across distances from 100 metres to over 100 miles and found that the time-distance relationship followed a consistent power law. The exponent of 1.06 was the best-fit value across this dataset. Independent analyses have confirmed the exponent falls between 1.05 and 1.07 for most competitive runners, with recreational runners tending toward 1.07–1.10 (meaning they slow down more than the formula predicts at longer distances).
The practical implication for recreational runners: The standard Riegel exponent of 1.06 was calibrated on competitive and elite performances. Most recreational runners — particularly those without structured long-run training or racing experience at the target distance — will slow more than predicted. Marathon predictions from 5K or 10K inputs routinely overestimate recreational runners' marathon capability by 5–15 minutes. The prediction is best treated as a ceiling, not a guarantee.
Accuracy: When to Trust the Prediction and When Not To
Race time predictions are not equally reliable across all input-to-target distance combinations. The accuracy band narrows as the prediction distance stays close to the input distance and widens as the gap grows.
Accuracy tiers:
| Input distance | Target distance | Typical accuracy | Notes |
|---|---|---|---|
| 10K | Half marathon | ±3–5% | Most reliable pairing |
| Half marathon | Marathon | ±3–6% | Reliable for trained runners |
| 5K | 10K | ±3–5% | Good |
| 10K | Marathon | ±5–8% | Optimistic for recreational runners |
| 5K | Half marathon | ±6–10% | Use with caution |
| 5K | Marathon | ±8–15% | Wide uncertainty; use as rough ceiling |
Conditions that cause the prediction to be optimistic (actual time slower):
- The input result was run on a flat, fast course; the target race is hilly
- Input result was a personal best in ideal conditions; target race in heat or wind
- Not completing regular long runs at the target distance — undertrained for the full distance
- First time racing at the target distance — unfamiliarity with pacing and fuelling
- Racing above your lactate threshold pace for the input distance (e.g., going out too hard in a 5K and suffering in the last kilometre)
Conditions that cause the prediction to be conservative (actual time faster):
- You are significantly fitter at the target distance than the input distance suggests (e.g., you have been doing specific marathon training but only have a 5K result)
- The input result was run on a difficult course or in bad weather
- You are a very experienced racer who optimises pacing at longer distances
The most reliable input: A recent race result (within 6–8 weeks) at a distance between one-half and two-thirds of the target distance tends to produce the most accurate predictions. A recent half marathon is the gold standard input for marathon prediction; a recent 5K is the gold standard for 10K prediction.
Prediction Tables: 5K Through Marathon
The following tables show Riegel predictions for common input times. All calculations use T₂ = T₁ × (D₂/D₁)^1.06.
Predicted times from 5K input
| 5K time | 10K | Half marathon | Marathon |
|---|---|---|---|
| 15:00 | 31:10 | 1:08:40 | 2:24:03 |
| 18:00 | 37:24 | 1:22:24 | 2:52:48 |
| 20:00 | 41:33 | 1:31:35 | 3:12:03 |
| 22:00 | 45:42 | 1:40:44 | 3:31:18 |
| 25:00 | 51:55 | 1:54:18 | 4:00:05 |
| 28:00 | 58:10 | 2:07:52 | 4:28:53 |
| 30:00 | 1:02:20 | 2:17:00 | 4:48:07 |
| 35:00 | 1:12:44 | 2:39:30 | 5:36:08 |
| 40:00 | 1:23:09 | 3:02:00 | 6:24:09 |
Predicted times from 10K input
| 10K time | 5K | Half marathon | Marathon |
|---|---|---|---|
| 35:00 | 16:50 | 1:17:20 | 2:42:40 |
| 40:00 | 19:14 | 1:28:23 | 3:05:57 |
| 45:00 | 21:38 | 1:39:26 | 3:29:14 |
| 48:00 | 23:05 | 1:46:06 | 3:37:21 |
| 50:00 | 24:02 | 1:50:36 | 3:52:13 |
| 55:00 | 26:26 | 2:01:39 | 4:15:30 |
| 60:00 | 28:51 | 2:12:42 | 4:38:47 |
| 70:00 | 33:39 | 2:34:48 | 5:25:21 |
| 80:00 | 38:28 | 2:56:54 | 6:11:55 |
Predicted times from half marathon input
| Half marathon | 10K | Marathon |
|---|---|---|
| 1:20:00 | 36:32 | 2:47:32 |
| 1:30:00 | 41:03 | 3:07:55 |
| 1:40:00 | 45:34 | 3:28:18 |
| 1:45:00 | 47:49 | 3:38:30 |
| 1:50:00 | 50:05 | 3:48:42 |
| 2:00:00 | 54:35 | 4:09:06 |
| 2:15:00 | 1:01:24 | 4:39:42 |
| 2:30:00 | 1:08:12 | 5:10:19 |
| 2:45:00 | 1:15:01 | 5:40:55 |
How to Use This Predictor (Step by Step)
Step 1 — Choose your input result carefully. The prediction is only as good as its input. Use a genuine race effort — not a comfortable training run — from within the past 6–8 weeks. Older results or training runs at sub-maximal effort will produce predictions that underestimate your current fitness (giving times that are too slow) or overestimate it if fitness has declined.
Step 2 — Enter distance in km. The calculator accepts any distance in kilometres. Standard distances: 5K = 5.000, 10K = 10.000, half marathon = 21.098, marathon = 42.195. Non-standard race distances (8K, 15K, 10 miles) work equally well — enter the exact distance.
Step 3 — Enter your finish time. Hours, minutes, and seconds. Use your chip time (net time), not gun time, for most accurate results. A gun-time result that includes a long start-pen wait can inflate the input by 1–3 minutes and make all predictions too slow.
Step 4 — Read all four predictions simultaneously. The predictor outputs 5K, 10K, half marathon, and marathon times together. Examine them as a set — if any prediction feels impossible given your current training, that signals a calibration issue with the input result (too good a course, unusual conditions) rather than a formula error.
Step 5 — Apply context adjustments. Before committing to a race goal, cross-reference the prediction against your training: have you completed long runs at 80–90% of the target race distance? Are you racing in comparable conditions to your input race? Have you been running consistently for at least 12 weeks? If not, add a conservative buffer of 3–8% to the marathon prediction.
Six Worked Examples Across Distances and Ability Levels
Example 1: 22-Year-Old Male, Predicting First 10K from Parkrun
He runs his local 5K parkrun in 22:30 (1,350 seconds) — a genuine maximal effort.
T₂ = 1,350 × (10 / 5)^1.06
= 1,350 × 2^1.06
= 1,350 × 2.085
= 2,815 seconds = 46:55
Predictions: 10K in 46:55 (4:41/km), half marathon in 1:43:07, marathon in 3:37:19.
Interpretation: A 22:30 5K runner can confidently target sub-47 minutes in their first 10K. The half marathon prediction of 1:43 is achievable if he has been running longer training runs. He sets a race goal of 47:30 — slightly conservative for a first 10K — and accepts that his marathon prediction (3:37) requires specific marathon training before it becomes realistic.
Example 2: 34-Year-Old Female, Half Marathon to Marathon
She has run two half marathons. Most recent result: 1:52:00 (6,720 seconds).
T₂ = 6,720 × (42.195 / 21.098)^1.06
= 6,720 × (2.000)^1.06
= 6,720 × 2.085
= 14,011 seconds = 3:53:31
Predictions: Marathon in 3:53:31 (5:33/km).
Interpretation: Her Riegel prediction is 3:53:31. She is targeting her first marathon and has followed a 16-week programme including four long runs of 30–35 km. Because she has completed the training and her half marathon result is recent, her coach advises targeting 3:55 as the race goal — slightly conservative, negative-split strategy. If she goes through the halfway point in 1:58, she is on track for a 3:54–3:56 finish.
Example 3: 47-Year-Old Male, Cross-Distance Validation
He ran a 10K in 55:00 (3,300 seconds) three weeks ago. He also ran a half marathon two months ago in 2:04:00 (7,440 seconds). He wants to know if both results are consistent.
From 10K:
HM prediction = 3,300 × (21.098 / 10)^1.06
= 3,300 × 2.193
= 7,237 seconds = 2:00:37
From half marathon:
10K back-prediction = 7,440 × (10 / 21.098)^1.06
= 7,440 × 0.456
= 3,393 seconds = 56:33
Interpretation: His 10K predicts a half marathon of 2:00:37, but he actually ran 2:04:00 — 3 minutes 23 seconds slower. And his half marathon back-predicts a 10K of 56:33, but he actually ran 55:00 — 93 seconds faster. The pattern suggests he is stronger at 10K relative to the half marathon — likely undertrained for the longer distance (insufficient long-run volume) rather than any problem with his 10K fitness. His Riegel coefficient from the half marathon is effectively ~1.08 rather than 1.06. For his marathon goal, he should use the half marathon result (2:04) as his input and accept the prediction of 4:17:10 as a realistic ceiling, not the 10K-derived 3:48.
Example 4: 29-Year-Old Female, Predicting from Non-Standard Distance
She races a 15K trail event and finishes in 1:14:30 (4,470 seconds). Her next race is a half marathon.
T₂ = 4,470 × (21.098 / 15)^1.06
= 4,470 × (1.4065)^1.06
= 4,470 × 1.434
= 6,410 seconds = 1:46:50
Predictions: Half marathon in 1:46:50 (5:03/km).
Note: The 15K was a trail run on hilly terrain. Her half marathon will be a road race on a flat course. Trail-to-road conversion typically improves performance by 5–10% for comparable effort — she adjusts the prediction: 1:46:50 × 0.93 (7% course correction) ≈ 1:39:12 as an adjusted road HM target. She sets a conservative goal of 1:42 for her first road half marathon.
Example 5: 55-Year-Old Male Masters Runner, Tracking Age-Group Fitness
He runs consistently and wants to monitor whether his fitness is holding or declining year over year. He runs a controlled 5K time trial each January.
| Year | 5K time | Marathon prediction |
|---|---|---|
| 2022 | 23:15 | 3:43:58 |
| 2023 | 23:42 | 3:49:17 |
| 2024 | 24:08 | 3:54:11 |
| 2025 | 23:55 | 3:51:33 |
Interpretation: The Riegel marathon prediction tracks his fitness trajectory precisely — a gentle decline from 2022 to 2024 followed by a partial recovery in 2025. He uses the calculator not to set literal marathon goals (he doesn't run marathons) but as a consistent, single-number fitness index that integrates all his training into one comparable metric. The prediction improved by 2 minutes 38 seconds from 2024 to 2025 despite no racing — confirming that his winter training block was productive.
Example 6: 38-Year-Old Female, Assessing Boston Qualifier Feasibility
The Boston Marathon qualifying time for women aged 35–39 is 3:45:00. She wants to know what half marathon time she needs to demonstrate Boston-viable fitness.
Working backwards from the target:
3:45:00 = 13,500 seconds
13,500 = T₁ × (42.195 / 21.098)^1.06
13,500 = T₁ × 2.085
T₁ = 13,500 / 2.085 = 6,475 seconds = 1:47:55
Interpretation: To have Riegel-predicted fitness for a 3:45 marathon, she needs a half marathon of approximately 1:47:55 or faster. Accounting for the typical 3–5% optimism of the Riegel prediction for recreational runners, a more conservative required half marathon is 1:44–1:46. She is currently running half marathons in 1:52 — she needs to improve by 5–8 minutes at the half before confidently targeting Boston qualification.
How to Adjust Predictions for Course and Conditions
The Riegel formula assumes equivalent conditions between the input and target race. When conditions differ, the raw prediction should be adjusted before being used as a race goal. The following corrections are approximate and based on sport science literature and race data analysis.
Course elevation:
- Add 8–10 seconds per km per 100m of net elevation gain for road running
- A 10K with 200m of net gain (typical hilly road race) → add 16–20 seconds/km → +2:40–3:20 to the predicted time
- Flat prediction → hilly race: multiply prediction by 1.03–1.06 depending on severity
- Hilly input → flat target: multiply prediction by 0.94–0.97
Temperature:
- Optimal racing temperature: 7–13°C
- Add approximately 1–2% per 5°C above 15°C
- At 25°C (warm): add ~3–4% to predicted time
- At 30°C+ (hot): add 5–8% or more depending on humidity
Wind:
- Significant headwinds slow pace meaningfully; tailwinds provide smaller benefit (aerodynamic asymmetry)
- Into a 20 km/h headwind: add ~2–3% to predicted time
- Direct tailwind of the same speed: subtract ~1% at most
Surface:
- Trail to road: multiply by 0.92–0.95 (trail is typically 5–8% slower than equivalent road effort)
- Road to track: multiply by 0.99 (track is marginally faster due to consistent surface and no traffic)
Combined adjustment example: Trail 15K (200m gain, 18°C) to flat road half marathon (12°C):
- Course correction (trail to road, flat): × 0.93
- Elevation correction (removing 200m gain): × 0.97
- Temperature correction (warm to cool): × 0.98
- Combined: raw prediction × 0.93 × 0.97 × 0.98 ≈ × 0.884
This means a raw prediction of 1:46:50 becomes approximately 1:33:51 after adjustments — a significant difference that illustrates why applying context matters more than the raw formula output.
Using Predictions for Goal-Setting and Training Targets
The race time predictor's most valuable use is not the number itself — it is the training targets that flow from it.
Training pace zones from a predicted race time: Once you have a predicted marathon time, divide by 42.195 to get your predicted marathon pace per km. Then use the following multipliers to derive specific training paces:
| Training run type | Pace relative to predicted marathon pace |
|---|---|
| Easy / recovery run | +1:30 to +2:30 per km |
| Long run (aerobic) | +0:45 to +1:30 per km |
| Marathon pace run | At predicted marathon pace ± 5 sec/km |
| Tempo / threshold | Marathon pace − 0:20 to − 0:35 per km |
| VO2 max intervals | Marathon pace − 0:50 to − 1:10 per km |
Example: Predicted marathon 3:53:31 → pace 5:33/km
| Run type | Target pace |
|---|---|
| Easy run | 7:03–8:03/km |
| Long run | 6:18–7:03/km |
| Marathon pace run | 5:28–5:38/km |
| Tempo | 4:58–5:13/km |
| VO2 max | 4:23–4:43/km |
Using the prediction as a fitness tracking tool: Regular time trials at a fixed distance (e.g., 5K parkrun every 4–6 weeks) produce a sequence of Riegel marathon predictions that track fitness change without requiring a marathon race. An improvement of 30 seconds in a 5K time trial corresponds to approximately a 2:30–3:00 improvement in the Riegel marathon prediction — a sensitive fitness signal from a short, low-cost test.
Setting A, B, and C race goals: Use the Riegel prediction as your A goal (best case, ideal conditions, well-trained). Set your B goal at Riegel + 3% (realistic, normal conditions). Set your C goal at Riegel + 6–8% (if conditions are difficult or training was interrupted). This three-goal structure prevents both overconfident pacing and unnecessary conservatism.
The Riegel Formula vs. Other Prediction Methods
Several other race time prediction methods exist alongside Riegel. Understanding their differences helps you choose the most appropriate approach for your situation.
Riegel formula (T₂ = T₁ × (D₂/D₁)^1.06): Single-input, empirically derived, works across all distances. Best for general race-to-race predictions with one known result. Exponent was calibrated on competitive/elite data.
Cameron's formula (alternate power law): A variant using a slightly different coefficient structure, generally producing very similar results to Riegel within ±1–2%. Used in some commercial calculators. The practical difference between Riegel and Cameron is smaller than the uncertainty in the input result.
Pete Riegel's age-graded approach: Riegel also developed age-graded tables (used by the World Masters Athletics Association) that adjust performance standards by age and sex. If you want to compare performances across age groups rather than predict absolute times, age-grading is more appropriate than the raw Riegel formula.
VO2 max-based prediction: Knowing your VO2 max (from a lab test or field estimate) allows race time prediction through the oxygen-demand equation for each distance. This method is more physiologically grounded but requires a VO2 max value. Our VO2 Max Calculator provides estimates from five different field tests.
Training-load-based prediction: Advanced training platforms (Garmin, TrainingPeaks, Strava) estimate race readiness from accumulated training stress, chronic training load, and fitness-fatigue ratios. These models are more accurate than single-race extrapolation but require months of logged data and are not accessible as a simple calculator.
Bottom line: For most recreational runners who want a quick, evidence-based prediction from a known race result, the Riegel formula is the appropriate tool. It performs well within two times the known distance, has been independently validated many times, and requires only two inputs.
Assumptions and Notes
- Formula source. Riegel, P.S. (1981). Athletic records and human endurance. American Scientist, 69(3), 285–290. PMID: 7235349.
- Fatigue exponent. Fixed at 1.06 — the best-fit value from Riegel's original analysis across world record performances at distances from 100m to 100+ miles. Independent meta-analyses confirm the exponent for trained runners falls between 1.05 and 1.07.
- Standard race distances. 5K = 5.000 km | 10K = 10.000 km | Half marathon = 21.098 km (IAAF standard) | Marathon = 42.195 km (IAAF standard).
- Input format. Enter net (chip) finish time from a genuine race effort within 8 weeks for highest accuracy.
- Recreational runner caveat. The Riegel exponent tends to understate pace degradation for untrained or recreational runners, particularly at marathon distance. Adding 3–8% to marathon predictions is advisable for runners without specific marathon training.
- No gender correction. This calculator uses the universal exponent of 1.06. Some implementations use 1.04–1.05 for women. The practical effect on predictions within 2× the input distance is small (< 2%).