How this calculator works
At a steady speed the rider supplies power to overcome four resistances. Rolling resistance equals the coefficient of rolling resistance times total mass times gravity, adjusted for the slope. Gravity along the road equals mass times gravity times the sine of the slope angle. Air drag equals half the air density times the drag area, or CdA, times the square of air speed relative to the bike. Each force is multiplied by road speed to get power, and the total is divided by drivetrain efficiency, the share of pedal power that reaches the rear wheel. Air density falls with altitude, so the same speed needs less power on a climb.
Formula
Angle = arctan(grade). Rolling force = Crr x total mass x g x cos(angle). Gravity force = total mass x g x sin(angle). Drag force = 0.5 x air density x CdA x air speed squared. Pedal power = (rolling + gravity + drag) x speed / drivetrain efficiency. Metabolic kcal = pedal power x seconds / (4,184 x 0.24).
Worked example
A 75 kg rider on a 10 kg bike at 30 km/h, hoods, slick tyres, asphalt, new chain, no wind and no grade: rolling force is 0.006 x 85 x 9.80665 = 5.0 N and drag force is 0.5 x 1.225 x 0.40 x 8.333 squared = 17.0 N. Wheel power is 22.0 x 8.333 = 183 W, and pedal power is 183 / 0.98 = 187 W. That is 2.50 W/kg and about 671 kcal over an hour.
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Frequently asked questions
Why does a headwind cost so much power?
Drag rises with the square of air speed, so a 10 km/h headwind turns 30 km/h into 40 km/h of relative air speed. The drag force rises by about 78 percent, and the power to overcome it rises further still.
How accurate are the position and surface values?
They are representative rather than measured for your bike. A tight jersey, wheel choice, tyre pressure and body shape can move CdA by 10 percent or more. Use the result to compare scenarios, not as a substitute for a power meter.
Does the calculator include acceleration?
No. It assumes a steady speed. Accelerating, cornering and changing pace add costs that a single average speed does not capture, which is one reason ride files often show higher normalized power than average power.
What cadence and gear should I use?
Power is the product of cadence and torque, so many combinations can produce the same watts. Choose a cadence you can sustain and use the bike cadence and speed page to see what each gear does at that cadence.