How this calculation works
On a climb, some power raises rider and bicycle against gravity, some rolls the tyres, and some pushes through relative air. The result separates these contributions, which is more informative than treating every watt as a function of slope alone.
Wheel power = speed × [m g sin(arctan grade) + Crr m g cos(arctan grade) + ½ρCdA vair|vair|]; positive crank demand = wheel power/efficiencyA worked example
For an 85 kg combined mass moving at 18 km/h on a five-percent grade, gravity contributes about 208.13 W. Rolling resistance adds about 20.81 W and still-air drag adds 30.625 W with the entered CdA and density. The total wheel demand is about 259.57 W, so ninety-five-percent drivetrain efficiency requires about 273.23 W at the crank. Increasing speed raises the still-air drag contribution sharply even while the gravitational force stays fixed.
Good to know
Steady speed with fixed coefficients; no acceleration, rider physiology, cornering, crosswind, traction, route forecast or braking recommendation. The number is a mechanical estimate, not a fitness diagnosis or guaranteed sustainable power. Real gradient variation, wind, surface and posture can change the result.
Reference: OpenStax — power and work rate (opens in a new tab) ↗
What this model answers
On a climb, some power raises rider and bicycle against gravity, some rolls the tyres, and some pushes through relative air. The result separates these contributions, which is more informative than treating every watt as a function of slope alone.
Road grade is rise divided by horizontal run, not an angle in degrees. The calculation uses the sine and cosine of arctan(grade), avoiding the assumption that the percentage itself is an angle. Road speed is measured along the slope.
The Bicycle spoke length geometry calculator concerns wheel component dimensions rather than rider effort. Neither a power estimate nor a spoke-length estimate establishes that a bicycle assembly is structurally suitable.
Measure the right inputs
Include luggage and carried equipment in rider-side mass, or account for them consistently in the bicycle mass. CdA, rolling coefficient and air density are entered conditions, not fitted automatically from a bike category.
Positive wind means a headwind aligned with the road; a negative value is a tailwind. Crosswind and yaw-dependent drag are outside this model. Efficiency applies between positive wheel demand and crank input, not to an independently measured electrical e-bike power.
Read the result in context
Aerodynamic opposing force uses relative air speed with its sign. A tailwind faster than the bicycle can assist motion in this simplified one-dimensional model. That contribution should not be forced positive just because drag usually resists a cyclist.
If the total wheel demand becomes negative, the metric reports ideal braking demand rather than negative pedaling output adjusted by drivetrain losses. It does not say a descent is safe or that actual brakes can absorb the predicted power continuously.
Work through the numbers
For an 85 kg combined mass moving at 18 km/h on a five-percent grade, gravity contributes about 208.13 W. Rolling resistance adds about 20.81 W and still-air drag adds 30.625 W with the entered CdA and density.
The total wheel demand is about 259.57 W, so ninety-five-percent drivetrain efficiency requires about 273.23 W at the crank. Increasing speed raises the still-air drag contribution sharply even while the gravitational force stays fixed.
Where the model stops
Steady speed with fixed coefficients; no acceleration, rider physiology, cornering, crosswind, traction, route forecast or braking recommendation.
The number is a mechanical estimate, not a fitness diagnosis or guaranteed sustainable power. Real gradient variation, wind, surface and posture can change the result.
A few questions, answered
Is five percent the same as five degrees?
No. Five percent means 0.05 rise/run; its road angle is arctan(0.05), approximately 2.86 degrees.
Why does efficiency only alter positive demand?
Negative wheel demand is reported as an ideal braking load. Applying a pedaling drivetrain efficiency to it would imply an unsupported braking or recovery model.