Cycling Power & Speed Simulator
Simulate steady cycling speed from power, gradient, headwind and drag assumptions, with a resistance breakdown and slope comparison.
Cycling physics inputs
Your cycling physics model
23.77 km/h · steady-state estimate
Wheel power balance: 194.00 W
Full result table
| Gradient (%) | Speed (km/h) | Climbing (W) | Rolling (W) | Air resistance (W) |
|---|---|---|---|---|
| 0 | 33.321318 | 0 | 38.577073 | 155.422927 |
| 2 | 23.770849 | 110.058846 | 27.514712 | 56.426442 |
| 4 | 16.740652 | 154.925288 | 19.365661 | 19.709051 |
| 6 | 12.382273 | 171.715063 | 14.309589 | 7.975349 |
| 8 | 9.693477 | 178.986943 | 11.186684 | 3.826373 |
| 10 | 7.932609 | 182.76477 | 9.138238 | 2.096992 |
| 12 | 6.706761 | 185.02337 | 7.709307 | 1.267323 |
| 15 | 5.44681 | 187.084982 | 6.236166 | 0.678852 |
| 20 | 4.161493 | 188.972919 | 4.724323 | 0.302758 |
Simplified steady-state physics, not a full Martin-model implementation. Level/uphill roads and along-road headwind only. Excludes acceleration, crosswind yaw, cornering, braking, altitude-dependent density changes and changing posture. Default drag and rolling values are assumptions.
Let’s work it out.
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How to use Cycling Power & Speed Simulator
- Enter total rider mass and bike/equipment mass separately.
- CdA combines frontal area and drag coefficient.
- The slope curve holds power and equipment constant.
Worked example
With 75 kg rider, 10 kg bike, 200 W crank power, 2% grade and the default resistance settings, the solver finds a speed whose rolling, climbing and aerodynamic powers sum to 194 W at the wheel.
Formula, accuracy & limitations
At steady speed v (m/s), wheel power = [m g sin(arctan(grade/100)) + Crr m g cos(arctan(grade/100)) + 0.5 ρ CdA (v + headwind)^2] × v. Wheel power = crank watts × efficiency/100. Speed is solved by bracketed bisection; g = 9.80665 m/s².
Simplified steady-state physics, not a full Martin-model implementation. Level/uphill roads and along-road headwind only. Excludes acceleration, crosswind yaw, cornering, braking, altitude-dependent density changes and changing posture. Default drag and rolling values are assumptions.
These outputs use the stated model and your supplied inputs. A mathematically consistent model can still differ from personal measurements. Scenario curves and formula comparisons are not statistical confidence intervals.
Read the research and method reference ↗Describe rider, equipment and road
Enter total rider mass and bike/equipment mass separately. Gradient is rise divided by horizontal distance, expressed as a percentage. This version supports flat roads and climbs, with a headwind along the road. It deliberately rejects downhill and tailwind scenarios instead of applying an inappropriate monotonic solver.
Set the resistance assumptions
CdA combines frontal area and drag coefficient. Crr describes rolling resistance, and density sets the air-mass assumption. Defaults are editable examples, not measurements of your setup. Crank power loses the chosen drivetrain fraction before reaching the wheel; the breakdown makes that loss visible.
Compare speed and power components
The slope curve holds power and equipment constant. The component chart shows wheel power spent against climbing, rolling and aerodynamic resistance. Drivetrain loss is shown separately. Matching the entered power balance checks the numerical solver, but does not validate your CdA or real road conditions.
Frequently asked questions
Does this include calories burned?
The model reports mechanical power and speed. Converting mechanical work to metabolic calories requires additional efficiency assumptions and is outside this tool.
Why are downhill and tailwind disabled?
Those cases can involve driving forces, coasting and multiple balance regimes. This solver is scoped to level/uphill roads with non-negative headwind.
Is the default CdA accurate for me?
It is an example assumption. Clothing, posture, rider size and equipment can change drag area, so compare scenarios or use measured data.
Why is wheel power below my entered watts?
The entered watts are crank power. Drivetrain efficiency reduces the power available to overcome road and air resistance.
