Methodology
Every number on this site comes from a formula printed on the page that uses it. This page gathers them in one place — the identities, the models, the constants and the checks — so you can verify any result yourself.
- Formulas stated in full
- Constants named, not buried
- Tested against hand-computed cases
Speed, pace, distance and time
The homepage solver and the stationary bike solver use the definitional identities: speed = distance ÷ time, pace = time ÷ distance, distance = speed × time, time = distance ÷ speed. Speed and pace are stored as one internal value and displayed both ways. Conversions use the exact definitions 1 mile = 1.609344 km and 1 mph = 1.609344 km/h. Times are parsed strictly — h:mm:ss or m:ss, with seconds under 60 — and inputs the parser cannot read exactly are rejected with an explanation rather than guessed.
Gearing and wheel circumferences
The gear speed calculator computes speed = (chainring ÷ cog) × circumference × cadence × 60 ÷ 1,000,000, with circumference in millimetres. Gear inches = ratio × (circumference ÷ π, converted to inches); development = ratio × circumference in metres. The circumference table (700×23c 2,096 mm through 29″ × 2.2 at 2,288 mm) is printed in full on the gear page. These are nominal published values; a roll-out under rider weight is the most accurate measurement of an individual tyre.
The power model
The watts to speed calculator implements the power-balance model of Martin et al. (1998): power at the wheel = ½ρCdA·v³ + Crr·m·g·v + m·g·grade·v, and pedal power = wheel power ÷ η. Constants: air density ρ = 1.225 kg/m³ (sea level, 15 °C), g = 9.81 m/s², drivetrain efficiency η = 0.97. Position presets (CdA 0.32 / 0.28 / 0.25 / 0.22) and surface presets (Crr 0.004 / 0.005 / 0.008) are labelled estimates from published ranges. The cubic is solved numerically by bisection to a precision far below display rounding. Wind is deliberately not an input: a single wind figure would pretend to a precision the weather never offers.
The erg cubic
Fan and flywheel ergs obey a cubic power law. The erg maker publishes the relationship for its bike erg as watts = 2.80 × (500 ÷ split)³, where the split is seconds per 1000 m; the inverse gives split from watts. The stationary page applies the published formula unchanged and labels its outputs as the erg’s own scale, not road equivalents.
Triathlon splits
The triathlon calculator adds five parts: swim (distance ÷ pace per 100 m), T1, bike (distance ÷ speed), T2, and run (distance × pace per km). Preset distances are the standard formats — Ironman 3.8/180/42.2 km, 70.3 1.9/90/21.1 km, Olympic 1.5/40/10 km, Sprint 0.75/20/5 km. Nothing is rounded between legs; the finish time is the exact sum, displayed to the second.
How the numbers are checked
I check the site the way I would want it checked as a rider. Every formula is first worked by hand on cases I can verify independently — 40 km in 1:20:00 is 30.0 km/h; a 50/17 gear on a 2,105 mm wheel at 90 rpm is 33.4 km/h; 200 W in the default power setup returns the modelled 34.0 km/h. Those cases are pinned in an automated test suite that runs before any change ships, alongside checks that every page’s questions and answers match its structured data exactly. When a reader reports an error, the report, the fix and the re-check are handled under the editorial policy.
Frequently asked questions
Which formula does the watts calculator use?
The power-balance model published by Martin and co-authors in the Journal of Applied Biomechanics (1998): pedal power equals aerodynamic drag plus rolling resistance plus gravity, divided by drivetrain efficiency. It was validated against measured road rides in the original paper.
Where do the wheel circumferences come from?
Standard published values for each ETRTO tyre size at typical pressures — the same figures cycling computers ship with. A roll-out measurement of your own tyre is more precise, which is why the gear page prints the table it uses.
How was the site checked?
Every calculator’s arithmetic is pinned by automated tests against hand-computed cases — a 40 km ride in 1:20:00 must return 30.0 km/h, 200 W in the default setup must return the modelled speed — and the whole suite runs again before any update ships.
Why does the erg use a cubic formula?
Because fan and flywheel resistance grows with the cube of speed. The erg maker publishes the exact relationship, watts = 2.80 × (500 ÷ split)³ for a split per 1000 m, and the stationary page applies it unchanged.
What should I not use these numbers for?
Anything where an error has consequences beyond a spoiled ride: race cut-off decisions should be checked against the official athlete guide, and power targets for medical rehabilitation belong with a clinician, not a website.
- Martin et al. — “Modeling road cycling performance” (PubMed) — the power-balance model and validation
- Sheldon Brown’s gear pages — gearing conventions and gain ratios
- Concept2 — official site — the published erg pace-to-watts relationship