Cycling Power Calculator
Work out the watts needed to hold a speed on any gradient, split into rolling resistance, air drag, gravity and drivetrain loss, from the Martin et al. model.
Cycling Power Calculator: with the default inputs, power required is 151 W.
Bike, bottles, tools and anything you're carrying.
Rise over run. 6% is a steady climb; 10% is steep.
Negative for a tailwind. Drag depends on air speed, not ground speed.
At the pedals, including drivetrain loss.
- Watts per kg of rider
- 2.02
- Rolling resistance
- 34.3 W
- Air drag
- 113.4 W
- Gravity (climbing)
- 0 WNegative on a descent — gravity is helping.
- Drivetrain loss
- 3.6 W
- Share of the work that is air drag
- 77%
- Total mass
- 185 lb
Assumptions
- Steady state at constant speed — no acceleration, braking or cornering losses.
- Headwind is taken as a pure head-on component; real crosswinds change effective CdA through yaw.
- Standard gravity 9.80665 m/s²; air density constant over the ride.
- Bearing, tyre-scrub and wobble losses are folded into Crr and CdA rather than modelled separately.
- Drivetrain efficiency is applied only when net power is positive; on a descent the model reports the negative wheel power directly.
| km/h | mph | Watts at the pedals | W/kg of rider |
|---|---|---|---|
| 15 | 9.3 | 32 | 0.43 |
| 20 | 12.4 | 58 | 0.77 |
| 25 | 15.5 | 97 | 1.29 |
| 30 | 18.6 | 151 | 2.02 |
| 35 | 21.7 | 226 | 3.01 |
| 40 | 24.9 | 322 | 4.31 |
| 45 | 28 | 445 | 5.94 |
On the flat, drag rises with the cube of speed: 10% more speed costs about 33% more watts.
How this is worked out
The formula
θ = arctan(gradient) F_gravity = m·g·sin θ F_rolling = Crr·m·g·cos θ P_wheel = (F_gravity + F_rolling)·v + ½·ρ·CdA·v_air²·v P_pedals = P_wheel ÷ drivetrain efficiency m = rider + bike mass (kg) g = 9.80665 m/s² v = ground speed (m/s) v_air = ground speed + headwind CdA = drag area (m²) Crr = coefficient of rolling resistance ρ = air density (1.225 kg/m³ at sea level, 15 °C)
Open How it’s calculated above to see this worked through with your own numbers.
What you enter
- Rider weight
- A number.in lb, kg, st · from 60 to 400 · defaults to 165
- Bike and kit weight
- Bike, bottles, tools and anything you're carrying.in lb, kg · from 5 to 100 · defaults to 20
- Speed
- A number.in km/h, mph, m/s · from 1 to 100 · defaults to 30
- Gradient
- Rise over run. 6% is a steady climb; 10% is steep.a percentage · from -25 to 25 · defaults to 0
- Headwind
- Negative for a tailwind. Drag depends on air speed, not ground speed.in km/h, mph, m/s · from -60 to 60 · defaults to 0
- Drag area CdA(under More options)
- Frontal area × drag coefficient. About 0.27 for a racer in the drops, 0.32 on the hoods, 0.40 sitting up, 0.23 on TT bars.from 0.15 to 1.2 · defaults to 0.32
- Rolling resistance Crr(under More options)
- About 0.004 for good clinchers on smooth asphalt, 0.008 on rough chipseal, 0.012 on gravel.from 0.001 to 0.03 · defaults to 0.005
- Air density(under More options)
- 1.225 at sea level and 15 °C. Roughly 1.06 at 1,500 m, 0.9 at 3,000 m.from 0.6 to 1.5 · defaults to 1.225
- Drivetrain efficiency(under More options)
- A clean chain loses about 2–3% between the pedals and the rear wheel.a percentage · from 80 to 100 · defaults to 97.6
What you get back
- Power requiredmain answer
- At the pedals, including drivetrain loss.
- Watts per kg of rider
- Rolling resistance
- Air drag
- Gravity (climbing)
- Negative on a descent — gravity is helping.
- Drivetrain loss
- Share of the work that is air drag
- Total mass
What this assumes
- Steady state at constant speed — no acceleration, braking or cornering losses.
- Headwind is taken as a pure head-on component; real crosswinds change effective CdA through yaw.
- Standard gravity 9.80665 m/s²; air density constant over the ride.
- Bearing, tyre-scrub and wobble losses are folded into Crr and CdA rather than modelled separately.
- Drivetrain efficiency is applied only when net power is positive; on a descent the model reports the negative wheel power directly.
About this calculator
Cycling has an unusually clean power equation. Four things take your watts — rolling resistance, air drag, gravity and the drivetrain — and each has a term you can write down. This calculator implements the model validated by Martin and colleagues in 1998, whose field measurements matched predicted power within a few watts across a range of speeds and gradients.
What each term does
- Rolling resistance is roughly proportional to speed and to weight, so it is a nearly constant background cost. At 30 km/h on good tyres it is typically 30–40 W.
- Air drag scales with the square of air speed for force and therefore the cube for power. This is the term that dominates: on the flat above about 25 km/h it accounts for the large majority of the work, and it is why going 10% faster costs roughly a third more power.
- Gravity is proportional to gradient, weight and speed. On anything above about 5% it swamps everything else, which is why climbing is a watts-per-kilogram problem and flat riding is a watts-versus-CdA problem.
- Drivetrain loss is a flat 2–3% of what you produce, dissipated in the chain and bearings.
Choosing CdA and Crr
These two inputs carry most of the model's uncertainty, so the defaults are conservative and adjustable:
- CdA (drag area) is around 0.23 m² for a rider on time-trial bars, 0.27 in the drops on a road bike, 0.32 on the hoods — the default — and 0.40 or more sitting upright. Martin et al. measured 0.27 for racing cyclists in a road position. Position matters far more than equipment: sitting up costs more watts than any wheel upgrade saves.
- Crr is about 0.004 for good clincher tyres on smooth asphalt, 0.005–0.008 on typical roads, and 0.012 or worse on gravel. Higher pressure is not automatically lower Crr — on rough surfaces very high pressure increases the losses.
- Air density falls with altitude and rises with cold. At 1,500 m it is about 1.06 kg/m³, which is worth several percent of speed for the same power — and part of why hour records are set at altitude.
Reading the results
The watts per kilogram figure is the standard currency of climbing. A trained amateur holds roughly 3–4 W/kg for an hour; 5 W/kg is strong club-racer territory; professional grand-tour climbers sustain around 6 W/kg. The share that is air drag tells you where to spend effort: if it is over 70%, position and clothing beat weight savings; if you are climbing and it is under 20%, only weight and fitness matter.
What the model leaves out
Steady state only — no acceleration, no braking, no cornering. It assumes a constant headwind exactly on the nose, when real wind arrives at an angle and produces yaw effects a single CdA cannot capture. Wheel bearing drag, tyre scrub in corners and the rider's own wobble are folded into Crr and CdA rather than modelled. And it says nothing about whether you can produce the number — only what physics demands.
Frequently asked questions
▸How many watts do I need to ride at 20 mph?
On the flat, in a road position on good tyres, roughly 200–230 W for a typical rider with a CdA near 0.32. Air drag is about 80% of that, so position changes the answer more than fitness does.
▸Why does a small speed increase cost so many watts?
Aerodynamic power rises with the cube of speed. Ten percent more speed needs about 33% more power against the air, and above roughly 25 km/h on the flat the air is most of what you are fighting.
▸What is CdA and what is mine?
Drag area — frontal area multiplied by drag coefficient, in square metres. Around 0.23 on TT bars, 0.27 in the drops, 0.32 on the hoods and 0.40 sitting upright. You can estimate your own from a measured power meter and this model.
▸How much does weight matter?
Almost nothing on the flat and enormously uphill. On a 6% climb, gravity is the dominant term, so a kilogram off the total mass is directly a percentage of the power required. On flat ground the same kilogram costs well under a watt.
▸Is this the power at the pedals or at the wheel?
At the pedals, which is what a crank or pedal power meter reads. The wheel figure is lower by the drivetrain loss — about 2.4% at the default efficiency.
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