Watts to speed calculator

How fast would those watts take you outdoors? And more usefully: what is taking them — the air, the road, or the hill?

## Why the same watts give wildly different speeds

Three things take your power, and they scale completely differently.

Air resistance rises with the cube of speed. Not the square — the force rises with the square, but power is force times speed, so the power you need goes up with the cube. Double your speed and you need eight times the power to push the air. This is why 200 watts gets you along nicely at 34 km/h and nowhere near 68.

Rolling resistance rises in a straight line with speed, and it is small. On a decent road with decent tyres it is usually ten to fifteen per cent of your total on the flat and falling as a share the faster you go.

Gravity does not care about speed at all. It takes a fixed number of watts per kilogram per per cent of gradient, whatever you are doing. That is why climbing is the great leveller: on a 10 per cent slope, air resistance has almost vanished and the entire contest is weight against power.

Move the gradient slider and watch the table at the bottom change. On the flat it is nearly all air. At 8 per cent it is nearly all gravity. That single shift explains most of what is confusing about cycling speed.

## What this means on a turbo trainer

It means the speed your trainer shows you is a fiction, and a useful one.

Indoors there is no air to push, no road to roll on and no hill to climb. Your trainer takes your power and applies a model — usually something close to the one on this page — to produce a plausible speed. Change the model's assumptions and the same watts give a different number, which is why two apps can disagree about how fast you just went.

So compare watts, not speed, between sessions. Watts is the thing you actually produced. Speed is an opinion about what those watts would have done somewhere else.

## The things this does not model

Wind. The calculator assumes still air. A headwind adds to the air you have to push as though you were going faster; a tailwind subtracts. Ten km/h of headwind at 30 km/h of road speed is the same work as riding at 40 in still air, which is why a windy day feels so disproportionately hard.

Acceleration. This is steady-state. Getting up to speed costs extra, and on a twisty course with a lot of braking it can cost a great deal.

Cornering, braking and draughting. Sitting in a group can cut your air resistance by a quarter to a half depending on where you are and how big the group is. That is the entire tactical basis of road racing.

Your real drag area. The CdA figures here are typical, not yours. Position, clothing, body shape and even helmet choice move it, and the difference between a flapping jacket and a close-fitting jersey is worth several watts at speed.

## Working backwards

The calculator solves for speed given power, but the interesting question is often the other way round: what would it take to hold 40 km/h? Set the power until the speed reads 40 and look at the number: on the flat, on the hoods, at 83 kg total, it takes about 320 watts, which is a long way past what most people can hold for any length of time — and that is the honest answer to why the people who do it look the way they do.