Watts, speed and the hill

A physics model of road cycling — aerodynamic drag, rolling resistance, gravity and drivetrain loss. Give it your power and see your speed, or give it a target speed and see the watts. Then change one thing and watch what it costs.

01 Your ride
Solve for
Weight
Speed
Your steady output for the effort you're picturing.
Positive uphill, negative downhill.
Bike, bottles, tools, clothing - everything but you.
Headwind positive, tailwind negative.
Advanced — aerodynamics, surface, air & drivetrain
Set by Riding position, or type your own.
Set by Tyres & surface, or type your own.
Temperature and altitude set the air density.
A clean modern chain runs about 97–98%.
02

The estimate

What went into this
How the model works

At a steady speed the power you put in goes entirely into overcoming four things: aerodynamic drag (which rises with the cube of speed — the big one on the flat), rolling resistance from the tyres, gravity when the road tilts up, and drivetrain loss in the chain.

This is the Martin et al. (1998) road-cycling power model. Solving it for speed needs a little numerical root-finding; solving it for power is direct arithmetic. It assumes a steady effort — no accelerating, no cornering — so treat it as a very good estimate, not a stopwatch.

Every constant — the CdA and Crr presets, drivetrain efficiency, the air-density formula — is sourced in this tool's research.md.