Cycling Power Calculator

Purpose

Estimate the steady-state rider power at the pedals required to hold a given speed at a given slope and wind. The model accounts for gravity, rolling resistance, aerodynamic drag, and drivetrain loss.

It assumes no acceleration, no drafting, no cornering or braking losses, and that any wind is purely a headwind or tailwind.

Inputs

Input	Meaning	Units
Rider weight	Body weight	lb
Bike + gear weight	Bike plus bottles, tools, clothing, etc.	lb
Speed	Ground speed	mph
Slope	Road grade (rise / run)	%
Wind	Positive = headwind, negative = tailwind	mph
Elevation	Above sea level; thinner air higher up	ft
Temperature	Local air temperature; cold air is denser	°F
Cycling fitness	Rough proxy for the rider's metabolic efficiency	—

Dropdown assumptions

Riding position → CdA (m²)

Upright / casual	0.55
Hoods (relaxed)	0.45
Hoods (moderate)	0.40
Drops	0.34
Aero bars / TT	0.26

Surface / tire → C_rr

Smooth pavement / road bike	0.0045
Average pavement / road bike	0.0055
Rough pavement	0.0070
Gravel	0.0120

These values bundle a typical road tire at a sensible pressure for the surface. Real-world rolling resistance also depends on tire width and pressure, and the relationship is surface-coupled: an over-pumped tire on rough chipseal can roll worse than a softer one because energy is wasted bouncing rather than rolling. A future version may model tire pressure, width, and surface together.

Air density ρ (kg/m³)

Computed from the entered elevation and temperature using the International Standard Atmosphere pressure profile and the ideal-gas law:

h is elevation in metres and T is the local air temperature in kelvins. Roughly: every 1000 ft of elevation thins the air by ~3%, and every 20 °F drop in temperature thickens it by ~4%. Humidity also shifts density — humid air is slightly less dense than dry air, since water molecules are lighter than the nitrogen and oxygen they displace — but the effect is ~1% in typical conditions and not modeled here.

Drivetrain efficiency η

Very efficient	0.98
Typical clean drivetrain	0.975
Slightly less efficient	0.97
Dirty / less efficient	0.96

Cycling fitness → metabolic efficiency e

Untrained	0.20
Recreational	0.22
Trained	0.24
Elite	0.26

Gross cycling efficiency varies with intensity, cadence, riding position, and how it's measured, so these four buckets are a rough proxy rather than a rider taxonomy. Pick the one that best matches your cycling-specific aerobic conditioning.

Constants

g	Gravitational acceleration	9.80665 m/s²
lb → kg	Pounds to kilograms	0.45359237
mph → m/s	Miles/hour to meters/second	0.44704

Unit conversions

The slope angle is recovered exactly from the entered grade:

An n% grade means n units of rise per 100 of run, so grade = tan(θ). Computing the angle once via atan keeps the formulas exact at any slope.

Power components

Total power required at the wheel is the sum of three terms; rider pedal power is wheel power plus drivetrain loss.

1. Gravity

Positive on a climb, negative on a descent.

2. Rolling resistance

The cos(θ) factor is the share of the rider's weight pressing the tire onto the road. On a steep slope, more of the weight points along the slope rather than into it, so the tire deforms a little less and rolling resistance drops slightly.

3. Aerodynamic drag

Drag force grows with the square of apparent wind speed, but the rider only does mechanical work at ground speed, so the power expression is v_air² · v_ground, not v_air³. With no wind those are identical; with wind, using v_air³ would over-charge a headwind and under-credit a tailwind.

This term grows quickly with speed and is usually the dominant one on flat ground.

4. Wheel power and pedal power

Drivetrain efficiency η is the fraction of the rider's pedal power that survives the chain, gears, and bearings to reach the wheel. It only applies while the rider is putting power in. On a descent steep enough to overcome rolling and aero drag, no pedaling is happening and there is no drivetrain loss to account for — required rider power is zero.

Calories burned

Pedal power is mechanical work, but the body has to spend more metabolic energy than that to produce it. The conversion goes through gross cycling efficiency e — the share of the rider's total metabolic energy expenditure during the ride that comes out of the pedals as mechanical work.

3600 / 4184 ≈ 0.8604 converts watt·hours to kcal: one watt sustained for one hour is 3.6 kJ of mechanical work, and one dietary kcal is 4184 J. Dividing by e marks up that mechanical number to the metabolic energy the body actually spent. With e = 0.24 (Trained) the multiplier is roughly 3.6, which is why you'll see the rule of thumb "kcal/hour ≈ watts × 3.6" on cycling apps.

This is a gross figure. Gross efficiency's denominator already includes the body's baseline burn during the exercise hour, so the displayed number is the metabolic cost of riding for an hour at this power — not "extra above sitting still." It's the same convention Strava, TrainerRoad, and Garmin use.

On a steep enough descent the calculator clamps pedal power to zero, so kcal/hour also shows zero. The rider is coasting — no muscular work is being done at the pedals, and there's nothing for this formula to mark up.

Treat the kcal/hour figure as long-run book-keeping: the energy the ride cost and that the rider eventually has to replace. Stored glycogen and fat mean a rider does not need to ingest this much during the hour itself.

What different conditions look like

Uphill

Gravity dominates as soon as the slope is more than a percent or two.

Flat road

Aerodynamic drag dominates. Because power scales with the square of apparent wind times ground speed, going a bit faster on the flat costs much more than the speed change suggests.

Headwind

Adds to apparent wind speed, so aero power grows fast.

Tailwind

Subtracts from apparent wind speed. If the tailwind is faster than the rider's ground speed, this calculator clamps apparent wind to zero. Physically the wind would push the rider forward, but this is a "power required" model and the honest answer in that regime is "you don't need to pedal." Modelling propulsion from a strong tailwind is out of scope.

Downhill

If gravity alone overcomes rolling and aero drag, P_wheel would be negative. Required rider power is reported as zero — you would coast. Holding the entered speed in that situation requires braking, which dissipates the surplus gravitational energy as heat. Brakes are not modeled.

Limits of the model

• No acceleration, stop/start, or cornering effects.
• Wind is purely head- or tailwind; crosswinds are not modeled.
• No drafting behind other riders.
• Tire pressure and width are baked into the surface category, not adjustable separately.
• Air density does not account for humidity (~1% effect).
• Rider-specific frontal area beyond the position dropdown is not modeled.
• Bearing losses beyond the drivetrain efficiency factor are not modeled.
• Braking power on descents is not quantified.
• Metabolic efficiency is treated as a single number per cycling fitness bucket. Real efficiency varies with intensity, cadence, and position within a single ride.