Free Running Pace Calculator — Pace · Time · Distance + Riegel Race Projections

What This Calculator Does

Every runner — from the casual park-jogger to the competitive amateur chasing a sub-3:00 marathon — eventually runs into the same three-cornered question: how fast, how far, how long?Two of those numbers determine the third, and getting the math right is the difference between a session that delivers exactly the adaptation you wanted and one that drifts into a training-stress no-man’s-land. This calculator is a three-way solver: feed it any two of distance, time, and pace, and it returns the third — together with average speed in km/h and mph, pace per kilometre, and pace per mile, all at once.

Layered on top is the Riegel race-time projection — the single most useful endurance-prediction equation in amateur running. Given a verified result at one race distance, Riegel projects what you can hold across all the other standard distances: a 24-minute 5K, a 50-minute 10K, a 1:51 half, a 3:53 marathon. The exponent of 1.06 encodes the empirical fact that pace decays slightly as distance rises, so you cannot simply scale linearly. The calculator runs the projection in both directions — extrapolate up from a short race, or interpolate down from a long one — and flags realistic versus aspirational targets.

Distance and pace come in either kilometres or miles — flip the unit toggle to match what your watch reads. The conversion (1 km = 0.621371 miles) happens in the background, and the output panel always shows both pace per km and pace per mile so you never have to do the multiplication in your head mid-session. Whether you train on a 400 m track, a measured 5 km loop, or an Imperial-units treadmill, the same target lands on the screen in the units you actually use.

The Math: Three-Way Solver + Riegel Projection

Pace is just a unit conversion problem until you reach race distances long enough for fatigue to bend the line. The calculator runs three simple algebra moves and one empirically tuned exponential — together they cover every common pace question.

The mechanical formulas — pace = time ÷ distance and its rearrangements — are truisms of unit algebra. The interesting one is Riegel. Pete Riegel, an American engineer, fitted the 1.06 exponent in 1981 against decades of race-result data and the relationship has held up across forty years of follow-up studies. The intuition is physiological: at very short efforts you are anaerobic-system-limited, at very long efforts you are glycogen-and-thermoregulation-limited, and the smooth power-law in the middle works because the same aerobic engine is doing the work across the 5K-to-marathon range. Riegel breaks down at the extremes — it over-predicts ultras (D > 50 km, where nutrition and pacing matter more than aerobic capacity) and under-predicts very short sprints (D < 1500 m, dominated by anaerobic power), but for the 5K-to-marathon band it is the most accurate single-equation projection in popular use.

The pace-versus-speed conversion is also worth keeping in working memory. 60 ÷ km/h = pace per km in minutes (so 12 km/h = 5:00/km), and pace per km × 1.609 = pace per mile. A 4:00/km runner is moving at 15 km/h, or about 9.32 mph, with a per-mile pace of 6:26. The calculator surfaces all four numbers — speed in km/h, speed in mph, pace per km, pace per mile — so you can sanity-check a watch reading against a treadmill display without re-running the conversion every time.

The 5 Standard Race Distances

Endurance racing has converged on five canonical distances, and Riegel projections are usually phrased between them. Knowing the exact distance to four decimal places matters for race-day pacing — a 100 m miscalculation over the marathon costs you a 27-second margin at 4:30/km pace.

• 5 km (5K, 3.10686 mi). The classic introductory race. Sub-25 minutes puts you in the active-fitness band, sub-20 minutes puts you in competitive-club territory, sub-15 minutes is national-class. Trains VO2 max and the upper end of aerobic capacity.
• 10 km (10K, 6.21371 mi). Doubles the distance, shifts the energy mix toward sustained aerobic power. Sub-50 is recreational-strong, sub-40 is competitive amateur, sub-30 is elite. Often used as a tempo-pace anchor in marathon training.
• Half marathon (21.0975 km, 13.1094 mi). The popular mass-participation distance. Sub-2:00 is the recreational milestone, sub-1:30 is competitive amateur, sub 1:10 is championship-level. Trains lactate-threshold endurance.
• Full marathon (42.195 km, 26.2188 mi).The historic distance, set by the 1908 London Olympics route. Sub-4:00 is recreational, sub-3:00 is competitive amateur (the “BQ” threshold for many age groups), sub-2:30 is elite. The Kelvin Kiptum men’s world record of 2:00:35 (Chicago, 2023) averages 2:51/km — a pace most amateurs cannot hold for one kilometre, sustained for forty-two of them.
• Ultras (50K, 100K, 100 mi, 24-hour).Beyond the marathon, fatigue and fuelling dominate over aerobic capacity. Riegel still projects roughly into 50K but progressively over-predicts at 100K and beyond — by the 100-mile mark, race times depend more on stomach tolerance, sleep deprivation, and night-time mental discipline than on your VO2 max. Use the calculator’s ultra projections as ceiling estimates only.

How to Use This Calculator

1. Pick your units — kilometres if you train metric, miles if you run imperial. The distance and pace fields relabel automatically and the output panel shows both unit systems regardless.
2. Pick the solver mode: pace from distance + time, time from distance + pace, or distance from time + pace. The disabled field locks and the other two open for input.
3. Enter the two known quantities. Distance accepts decimals (21.0975 for a half marathon); time accepts hh:mm:ss; pace accepts mm:ss per km or per mile. Be precise — at race pace, a 5-second-per-km miscount costs you 3:30 over a marathon.
4. Read the headline: the third number in your chosen unit, plus the conversion to the other unit, plus average speed in km/h and mph. The verdict line tells you what fitness band the result lands in.
5. Scroll to the Riegel projection panel. It auto-projects your input onto the four other standard race distances using the 1.06 exponent. Use the projected times as goal-setting anchors — if you ran 25:00 for 5K and the calculator projects 3:55 for the marathon, that is the time a comparable aerobic engine should deliver on a flat course in good conditions.

Three Worked Examples

Three runner archetypes, with the inputs and outputs spelled out so you can verify the calculator’s arithmetic by hand.

Example 1 — Recreational runner: 10 km in 50:00

You ran 10 km in 50:00 on a flat parkrun-style course. Solver mode: pace from distance + time. The calculator returns:

• Pace per km: 50:00 ÷ 10 = 5:00/km
• Pace per mile: 5:00 × 1.609 = 8:03/mi
• Average speed: 60 ÷ 5 = 12 km/h (7.46 mph)

That is a textbook recreational-runner result — comfortably below the sub-50 fitness milestone, holding a steady aerobic effort. The Riegel projections (T₂ = 50 × (D₂/10)^1.06) give:

• 5K: 50 × (5/10)^1.06 = 50 × 0.4796 = ≈ 24:00
• Half marathon: 50 × (21.0975/10)^1.06 = 50 × 2.222 = ≈ 1:51:06
• Full marathon: 50 × (42.195/10)^1.06 = 50 × 4.638 = ≈ 3:51:54

These are realistic ceilings for a runner whose 10K sits at 50:00 — meaning, if you trained appropriately for the longer distance and showed up healthy on race day, you should be in striking distance of those targets. Most amateurs miss their marathon Riegel projection by 5-15 minutes because long-run volume, fuelling discipline, and pacing execution are not free — but the 5K and half-marathon projections track closely if your weekly mileage is reasonable for the distance.

Example 2 — Competitive amateur: half-marathon at 4:30/km target

You are training for a half marathon and want to hold 4:30/km across the 21.0975 km distance — a typical competitive-amateur target putting you under 1:35. Solver mode: time from distance + pace. The calculator returns:

• Total time: 21.0975 × 4:30 = 21.0975 × 270 seconds = 5,696 seconds = 1:34:55
• Pace per mile: 4:30 × 1.609 = 7:14/mi
• Average speed: 60 ÷ 4.5 = 13.33 km/h (8.29 mph)

The 1:34:55 finish puts you firmly in the sub-1:35 competitive-amateur club — a goal time many trained runners chase for years. The verdict line should flag “competitive amateur” or similar; this is not a recreational target. To hold 4:30/km for 21 km you need a sustained heart-rate effort in the upper Zone 3 / lower Zone 4 range — pair this pace target with the heart rate zone calculator to find the bpm window your aerobic engine should be sitting in for a half-marathon-pace effort. The Riegel projection from this result extrapolates a marathon time of roughly 3:18: 1:34:55 × (42.195/21.0975)^1.06 = 1:34:55 × 2.085 ≈ 3:17:54.

Example 3 — Casual fitness Z2 long run: 1 hour at 6:30/km

You have one hour blocked for an easy aerobic-base run, and your Zone 2 pace lands at 6:30/km. Solver mode: distance from time + pace. The calculator returns:

• Distance: 3,600 seconds ÷ 390 seconds-per-km = 9.23 km
• Distance in miles: 9.23 × 0.621371 = 5.74 mi
• Average speed: 60 ÷ 6.5 = 9.23 km/h (5.74 mph)

That is a clean Z2 long run for a recreational runner — the conversational, easy-effort kind that builds mitochondrial density without depleting the legs for the next hard day. At 6:30/km you can hold full sentences mid-effort (the “talk test”), the fuel mix sits in the high-fat-oxidation band, and the session is the kind of polarized-training 80% volume the modern endurance literature wants you spending the bulk of the week in. Pair this pace target with the heart rate zone calculator Z2 bpm window and the calorie / TDEE calculator if the long run is part of a fat-loss-while-training plan — protein-rich recovery feeding from the protein intake calculator closes the loop on what 9 km in Zone 2 actually costs your body.

Common Mistakes

• Treadmill pace vs outdoor pace. Belt-driven treadmills assist your stride — the belt is moving under you whether you push hard or not, so the calorie cost and metabolic load of a 5:00/km treadmill run is meaningfully lower than 5:00/km on a road. The standard fix is a 1-2% incline on the treadmill to neutralise the assist; without it, expect treadmill paces to feel ~10-15 seconds-per-km easier than outdoor equivalents at the same heart rate.
• Ignoring elevation. A flat course Riegel projection assumes a flat race. Naismith’s rule — add 1 minute per 10 m of climb — gives you a first approximation for hilly terrain. A 300 m climb over a half marathon adds ~30 minutes to a flat projection, which is the difference between a PB attempt and a painful sufferfest. Trail-marathon Riegel projections are essentially useless without an elevation correction.
• Running threshold pace on easy days.The most common amateur error is letting easy-day pace creep up into Zone 3 because it “feels productive.” The calculator will happily compute a 4:50/km pace for your 10 km easy run — but if your aerobic-base pace should be 6:00/km, you have just turned a recovery session into a tempo. Pair pace with HR or RPE: easy means easy, and the pace number on the watch is the output of effort, not the input.
• Using a 5K → marathon Riegel projection. Riegel works best across adjacent distances (5K → 10K, 10K → half, half → full). Projecting from 5K straight to the marathon multiplies your decay assumptions across an 8.4× distance jump and overstates what your aerobic engine will sustain on race day. Realistic marathon predictions need a recent half-marathon result or — better — a long-run pace you have actually held for 25-30 km in training.
• Not adjusting for heat and humidity. Above ~20°C ambient, race times deteriorate by roughly 1-3% per 5°C. A 3:30 marathon at 10°C may slip to 3:38 at 25°C. Humidity compounds the effect by reducing evaporative cooling. Riegel projections assume neutral conditions; if your race day forecasts heat, mentally add 5-10 minutes to your goal time and adjust pace from gun, not from kilometre 30.
• Mixing per-km and per-mile pace inputs.A 4:30 input is a competitive half-marathon pace if interpreted as min/km, but a recovery-run pace if interpreted as min/mile. Always confirm the unit on the input field — the calculator’s unit toggle relabels the field, but if you copy a pace from a coach’s plan written in imperial units while the calculator is in metric, the output is meaningless. One of the most common silent errors in amateur training-pace math.
• Trusting the watch’s instantaneous pace under tree cover or in tunnels. GPS jitter under canopy can make instantaneous pace swing by 30+ seconds-per-km even while your effort is rock-steady. Use lap-pace or 1 km auto-splits as the truth, not the live readout. The calculator gives you the target; the watch’s job is to tell you whether you hit it over the lap, not to second-guess every stride.

When This Calculator Decides For You

1. Whether your goal time is realistic from current fitness.Run the Riegel projection from your most recent verified race or all-out time-trial. If you ran a 25:00 5K six weeks ago, your honest marathon ceiling is roughly 3:55 — chasing 3:30 off that base is a fitness-jump, not a pacing decision. The calculator settles the “is this realistic” question before you commit to a training block.
2. What target pace to lock in for a tempo run. Tempo intervals run at roughly 10K-to-half-marathon pace depending on duration. Plug your verified 10K pace into the calculator, read off the per-km number, set the watch alert to ±5 seconds of that pace. The session prescription stops being subjective — you have a hard target band to hit.
3. Sanity-check your watch’s pace before relying on it.Run a measured 1 km loop on a track, time it manually, then compare against the watch’s reported pace. If they disagree by more than 5%, the watch’s GPS is mis-calibrated for your stride or has a stale satellite cache. The calculator’s manual time-÷- distance gives you the truth your wrist may not be telling you.
4. Estimating finish time mid-race.Crossed the half-way mat at 1:48 in a marathon? Plug 21.0975 km and 1:48:00 into the calculator: pace = 5:07/km, projected finish at constant pace = 3:36, Riegel-corrected for late-race fade = 3:39-3:42. The gap between your watch’s naive projection (assumes constant pace) and the Riegel-corrected one (assumes realistic fade) is often the gap between the goal you announced and the result you actually run.
5. Building negative-split race plans.Negative splits — running the back half faster than the front — yield faster overall finish times and lower late-race blow-up risk. Set your target time, run the calculator at slightly slower pace for the first half (say, +5 seconds-per-km on goal pace), then verify the back-half pace needed to hit the total. If the back-half target lands in the “impossible” zone for your current fitness, the goal time itself is the problem, not the split strategy.

What This Calculator Doesn’t Model

• No elevation gain math.Hills are silent in the equations. A 4:30/km flat-pace target is meaningless on a course with 600 m of climbing — you need to layer Naismith’s rule (1 min per 10 m gained) or a course-specific elevation correction on top. For trail running and hilly road races, treat the calculator’s output as a flat-equivalent reference, not a course-specific finish-time prediction.
• No DST or timezone considerations.Race-day jet lag and disrupted sleep from a time-zone shift can shave several percent off race performance, and the calculator does not adjust. If you fly across >3 timezones for a race, plan to land 5-7 days early and use perceived-effort over pace targets for the first 48 hours.
• No cycling-specific Riegel exponent.Riegel’s 1.06 was fitted on running data. Cycling pace decays differently with distance because aerodynamic drag scales nonlinearly with speed, drafting matters, and gear-ratio changes the work-per- revolution relationship. Cyclists should use a power-curve model (W’) or a cycling-specific calculator, not a running pace projection.
• No heart rate or power data.Pace is a coarse proxy for effort. On hot days, in headwinds, on tired legs, or after a poor night’s sleep, the same pace costs you 10-20 bpm of additional cardiovascular load. The calculator does not ingest HR or running-power data; pair it with the heart rate zone calculator for intensity prescription that adjusts to how you feel today.
• No environmental adjustments — heat, altitude, wind. Riegel assumes neutral conditions: ~10-15°C, sea level, calm wind, dry course. Heat above 20°C, altitude above 1500 m, headwind above ~15 km/h, or rain/snow all degrade pace by 1-5% each, and they compound. The calculator will not warn you that your 3:30 marathon target is actually a 3:45 marathon target on a 28°C day in Mexico City; the environmental correction is yours to apply.

Pair this calculator with the heart rate zone calculator for the bpm window each pace target lands in — pace tells you how fast, HR tells you how hard, and a session that hits both is the canonical training prescription. The calorie / TDEE calculator closes the loop on energy balance: an honest weekly-mileage figure feeds straight into the activity multiplier and tells you whether your fat-loss-while-training plan is mathematically possible. The protein intake calculator covers the recovery-fuel side, and the ideal weight calculator sets the long-term body-composition anchor that running pace ultimately scales with — every kilogram of unnecessary mass is roughly 2-3 seconds-per-km of marathon time. Browse the full health calculator hub for the rest of the toolkit. Pace is the lingua franca of endurance training; everything else is the body that produces it.