About

Bike math, done properly.

PedalToolbox exists because cycling's numbers are settled science scattered across marketing. The physics has been published for decades. What's been missing is one set of tools that applies it carefully, remembers your bike, shows its working, and tells you the truth even when the truth is "you don't need to buy anything."

Why this site exists

Ask the internet a bike question with a number in it and you'll get three kinds of unhelpful answer. The shop-adjacent calculator sizes you toward what's in stock. The marketing quotes savings measured at speeds you'll never hold. And the genuinely good tools are scattered one per site — a pressure calculator here, a gear chart there — each starting from zero, none remembering the bike you told the last one about.

Meanwhile the actual math is public and has been for years — the power equation was validated in a journal in 1998, the training zones are in a book, the fit formulas are older than most readers. It just needs implementing with care, connecting together, and explaining without an upsell attached.

Who's behind it

PedalToolbox is built and written by Brian Hamilton and published by Hamilton Digital Media Limited, a small UK company that also publishes puzzle sites and the rest of the Toolbox family of calculator sites — pools, brewing, aquariums, RVing and sports betting, each built the same way as this one.

I'm not a professional bike fitter or a race mechanic, and I'm not going to pretend to be one. I'm a software developer with an internet engineering degree and thirty years of building things, including mathematical models for sports-prediction companies — work where a formula that's slightly wrong costs someone real money, quickly. Calculation tools are the job, and this site is that job pointed at bicycles.

I think that's the right qualification for this particular job, and here's the honest reasoning: most cycling numbers are physics problems wearing lycra. The equations are settled and published. What goes wrong in practice isn't the science — it's arithmetic applied sloppily, calculators that ignore what the marketing wants ignored, and advice shaped by what the person giving it happens to sell. Those are engineering and integrity problems, and they're the ones I can actually fix.

Where genuine domain expertise is required — a bike fit for persistent pain, safety-critical wrenching — the site says so and points you at the people who have it. And where a formula is a starting point rather than an answer, the page says that too, rather than rounding up to confidence.

How you can trust the numbers

Not "trust us" — here's the mechanism, and you can check every part of it yourself.

Published models, cited

The physics is the validated Martin et al. (1998) power equation; pressures follow the 15% tire-drop standard; zones are Coggan/Allen; fit formulas are the classics (LeMond, Hamley), named on the page. Nothing is a mystery multiplier.

One engine per domain

Every tool that touches gearing calls one gearing engine; every speed, climb and e-bike number comes from one physics engine. Two pages on this site physically cannot disagree about the same bike, because there is only one implementation of each formula.

200+ automated checks, pinned to reality

The engines run an automated test suite on every change — including real-world validation pins: 6 W/kg up Alpe d’Huez computes to ~40 minutes, zone boundaries reproduce published tables, and 700×25 rollout lands on the number printed on every bike-computer chart.

The working is shown

Every result has a "show the math" panel with the actual arithmetic, in your units. You should never have to take a number on trust — and if the reasoning looks wrong, you can see exactly where.

The sources we build on

The science here isn't ours and we don't claim it. Riding physics follows Martin et al., "Validation of a Mathematical Model for Road Cycling Power" (Journal of Applied Biomechanics, 1998). Tire pressure builds on the 15% tire-drop standard from Frank Berto's work, with rim limits from the ETRTO standards. Training zones and power profiling come from Coggan and Allen's Training and Racing with a Power Meter. Gearing conventions are the ones Sheldon Brown documented; fit formulas are Greg LeMond's and Hamley & Thomas's, named where used. Sizing charts and component data follow manufacturers' published specifications.

  • Martin, J. C. et al. (1998). Validation of a mathematical model for road cycling power. Journal of Applied Biomechanics, 14(3), 276–291. doi:10.1123/jab.14.3.276
  • Martin, J. C. & Spirduso, W. W. (2001). Determinants of maximal cycling power: crank length, pedaling rate and pedal speed. European Journal of Applied Physiology, 84, 413–418. doi:10.1007/s004210100400
  • Jeukendrup, A. (2014). A step towards personalized sports nutrition: carbohydrate intake during exercise. Sports Medicine, 44 (Suppl 1), 25–33. doi:10.1007/s40279-014-0148-z
  • American College of Sports Medicine (2007). Exercise and fluid replacement (position stand). Medicine & Science in Sports & Exercise, 39(2), 377–390. doi:10.1249/mss.0b013e31802ca597
  • Ainsworth, B. E. et al. (2011). 2011 Compendium of Physical Activities. Medicine & Science in Sports & Exercise, 43(8), 1575–1581. doi:10.1249/MSS.0b013e31821ece12
  • Allen, H. & Coggan, A. Training and Racing with a Power Meter (VeloPress) — the seven-zone model, the matching heart-rate levels and the power-profile benchmarks.
  • Friel, J. The Cyclist's Training Bible (VeloPress) — the seven LTHR-based heart-rate zones and the 30-minute threshold test.
  • Tanaka, H., Monahan, K. D. & Seals, D. R. (2001). Age-predicted maximal heart rate revisited. Journal of the American College of Cardiology, 37(1), 153–156. doi:10.1016/S0735-1097(00)01054-8
  • Robergs, R. A. & Landwehr, R. (2002). The surprising history of the "HRmax = 220 − age" equation. Journal of Exercise Physiology Online, 5(2), 1–10 — the ±10–12 bpm scatter around every age formula.
  • Sheldon Brown, Gear theory and gear calculator — ratio, gear-inch and development conventions; Gain ratios — the gain ratio and its worked examples.
  • USA Cycling, Junior gear restrictions — the junior track rollout limits; road.cc, the UCI's maximum gear test (June 2025) — the 10.46 m cap and its 54×11 equivalence.
  • ETRTO — rim and tire standards, including the hookless pressure limit.
  • Shimano and SRAM dealer / technical manuals (si.shimano.com, sram.com/service) — the torque figures for their own components; Park Tool, Torque Specifications and Concepts — the cross-brand compilation for stems, seatposts and bottom brackets.

Our contribution is the implementation, the testing, the connections between tools — and a stubborn insistence on showing the arithmetic so you're never asked to take a number on faith.

Your data, briefly

The Garage saves your bikes in your own browser's local storage — nothing is sent to us, there are no accounts, and the privacy policy is short because there's genuinely little to govern. A working erase-everything button lives on both pages.

Corrections are welcome — genuinely

A site whose entire promise is "the numbers are right" has to mean it, which means being easy to correct. If you find a mistake — in a calculation, a formula, a chart, or a fact in an article — [email protected] goes straight to a person. We'll fix it quickly and note on the page what changed and when. No defensiveness, no quiet edits.

That's not politeness. Standards get revised, components get reformulated, and physics has assumptions. A correction channel that people actually use is the cheapest quality control there is.

How the site makes money

Eventually, some links to products may earn a commission at no cost to you — that's the whole model. No ads that follow you around, no paid reviews, no sponsored placements, and nothing gated behind a signup. The rules we hold ourselves to are written down in the affiliate disclosure — including the standing commitment to say so when the free option wins, which on a bike it very often does.