Cycling Hill Climb Power Calculator

The Three Power Components

Cycling power on a climb comes from three sources: lifting your mass against gravity, overcoming rolling resistance, and pushing through aerodynamic drag.

Gravity (the Dominant Term)

P_gravity = total_mass_kg x 9.81 x speed_m/s x sin(arctan(grade/100))

Once a climb is steep enough to slow you down, gravity takes over almost completely. At 5% and 10 km/h a 75 kg rider on a 9 kg bike spends about 114 watts on gravity alone, against 11 for rolling resistance and 6 for air, so gravity is 87% of the job.

Below about 4% the picture changes faster than people expect, because you are moving quickly enough for air resistance to matter again. At 3% and 25 km/h that same rider is only spending about 65% of their power on the climb itself and a quarter of it on the air.

Rolling Resistance

P_rolling = total_mass x 9.81 x Crr x speed_m/s

Crr is the rolling resistance coefficient: roughly 0.004 for supple road tires on smooth pavement, up to 0.012 for off-road conditions. This calculator uses 0.005 as a road tire default.

Aerodynamic Drag

P_aero = 0.5 x air_density x CdA x speed_m/s cubed

CdA (drag coefficient times frontal area) for a road cyclist in a normal riding position is roughly 0.32 m2. At climbing speeds below 15 km/h, aero drag is typically under 10% of total power. At faster climbing speeds on a descent or false flat, it becomes significant.

Effort Zones

Power divided by body weight gives watts per kilogram. Under 2.5 W/kg is easy endurance. 2.5 to 3.5 W/kg is steady endurance. 3.5 to 4.5 W/kg is tempo to threshold. Above 4.5 W/kg is threshold to VO2 max territory. Elite climbers sustain 6+ W/kg on race climbs.

Using the Results

This is a useful tool for pacing unfamiliar climbs. Enter the grade and your target speed to see whether the required power is within your sustainable range. Adjust speed down until the required power matches what you can actually hold.