About

Cycling power is the rigorous application of physics to human endurance. Unlike running, where energy expenditure is roughly linear with speed, cycling involves overcoming three primary forces: Aerodynamic Drag, Rolling Resistance, and Gravity. The relationship between speed and power is non-linear; specifically, overcoming air resistance requires power proportional to the cube of speed. This means riding at 40 km/h requires significantly more than double the power of riding at 20 km/h.

This calculator utilizes the standard equation of motion for a cyclist. It accounts for environmental variables like Air Density (ρ) derived from elevation and temperature, and mechanical variables like Drivetrain Efficiency (η). Whether you are targeting a specific time trial result or analyzing a climb, this tool provides the theoretical wattage required to maintain a steady state velocity.

Formulas

The total power P required at the pedals is the sum of power needed to overcome all resistive forces, divided by drivetrain efficiency.

P = (F_gravity + F_rolling + F_drag) × v1 - Loss_dt

1. Gravity Force: The component of weight pulling the rider back down the slope.

F_gravity = g ⋅ sin(arctan(slope)) ⋅ m_total

2. Rolling Resistance: Friction from tire deformation against the road surface.

F_rolling = g ⋅ cos(arctan(slope)) ⋅ m_total ⋅ Crr

3. Aerodynamic Drag: The force of air resistance, proportional to air density and the square of air speed.

F_drag = 0.5 ⋅ CdA ⋅ ρ ⋅ (v_bike + v_wind)²

Reference Data

Variable	Symbol	Typical Value (Road)	Impact Factor
Air Density	ρ	1.225 kg/m³	Decreases with altitude. 1000m elevation reduces drag by ~10%.
Drag Area	CdA	0.30 - 0.40 m²	Major factor at speeds > 25km/h. Reduced by body position (Drops/Aero).
Rolling Resistance	Crr	0.003 - 0.005	Linear resistance. Depends on tire pressure and road surface quality.
Drivetrain Loss	Loss	2% - 5%	Mechanical friction in chain, bearings, and derailleur pulleys.
Gravity	g	9.81 m/s²	Dominant factor on climbs > 5% grade.

Frequently Asked Questions

This is due to Aerodynamic Drag. While Rolling Resistance and Gravity (on a constant slope) scale linearly with speed, Air Resistance scales with the square of speed. Since Power = Force × Speed, the power required to overcome air resistance scales with the cube of speed. Going from 30km/h to 40km/h requires nearly double the power, not just 33% more.

CdA is a measure of your aerodynamic efficiency. For a typical road cyclist on the hoods, it ranges from 0.30 to 0.35. In the drops, it might lower to 0.25-0.30. A time trial (TT) position with aero bars can bring this down to 0.20-0.25. Loose clothing significantly increases this number.

Surprisingly little. On a purely flat road, weight only affects Rolling Resistance, which is a small fraction of total resistance at speed. However, Aerodynamic Drag (CdA) often correlates with body size (surface area), so a heavier rider often has a higher CdA, but not always linearly.

We use the Barometric Formula. Air density (rho) is calculated based on your input Elevation and Temperature. Higher altitudes and higher temperatures result in thinner air (lower density), which reduces aerodynamic drag and increases speed for the same wattage.

No chain system is 100% efficient. Mechanical friction occurs in the chain links, derailleur pulleys, and bottom bracket. A clean, high-end drivetrain loses about 2-3% of power (efficiency 97-98%). A dirty or worn chain can lose 4-6% or more.