Watts to Speed Calculator (Cycling Power to MPH or km/h)

Estimate how fast you ride in mph or km/h from cycling power in watts, or the watts needed for a target speed, with typical bike drag and tire presets.

Solve for

Steady straight-line road model; the optional settings start at typical road-bike values.

Drivetrain input power (W)

Total moving mass

Rider plus bike, or total vehicle and load.

Road grade (%)

Blank = level (0%). Positive uphill; negative downhill.

Speed result unit

Drag, surface, wind and drivetrain

Drag-area preset

Illustrative cycling presets; use measured CdA for a specific rider or vehicle.

Custom CdA (m²)

Rolling-resistance preset

Custom rolling coefficient Crr

Along-road wind

Blank = calm. Positive headwind; negative tailwind. Crosswind is excluded.

Air density (kg/m³)

Blank = 1.225 kg/m³ (standard sea-level density).

Drivetrain efficiency (%)

Blank = 97%. Applied to positive drive power.

Watts to Speed Formula

The formula below is the drag-only special case: calm air, level road, zero rolling resistance and 100% drivetrain efficiency. The calculator also models rolling and grade forces, wind and drivetrain losses; those defaults will give different results.

S = ((2 · P) / (Cd · A · ρ))1/3

Variables:

S is the speed (m/s)
P is aerodynamic power at the wheel in this special-case formula (watts); the widget uses input power before drivetrain loss.
C_d is the drag coefficient (dimensionless)
A is the frontal area (m²)
ρ is the air density (kg/m³)

For the drag-only case, take that cube root. The full road model instead balances P × η = v × [½ρCdA(v + w)|v + w| + Crr m g cosθ + m g sinθ], with θ = atan(grade/100) and positive w for headwind. When the balance is negative at a target speed, the result identifies required braking at the wheel.

Watts to Speed Conversion Table (Cd = 0.80, Area = 0.40 m², ρ = 1.225 kg/m³)
Power (W)	Speed (m/s)	Speed (km/h)	Speed (mph)
50	6.34	22.83	14.19
75	7.26	26.14	16.24
100	7.99	28.77	17.87
125	8.61	30.99	19.25
150	9.15	32.93	20.46
175	9.63	34.67	21.54
200	10.07	36.24	22.52
225	10.47	37.69	23.42
250	10.84	39.04	24.26
275	11.20	40.30	25.04
300	11.52	41.49	25.78
325	11.84	42.61	26.48
350	12.13	43.68	27.14
375	12.41	44.69	27.77
400	12.68	45.66	28.37
450	13.19	47.49	29.51
500	13.66	49.19	30.57
600	14.52	52.27	32.48
700	15.29	55.03	34.19
800	15.98	57.53	35.75
Assumes level road, steady-state aerodynamic power only. Formula: v = [(2 × P) / (Cd × A × ρ)]^(1/3). Here Cd = 0.80, A = 0.40 m² (CdA = 0.32 m²), ρ = 1.225 kg/m³; wind and rolling resistance are zero and efficiency is 100%.

What is the Relationship Between Watts and Speed?

The relationship between watts and speed is determined by the power required to overcome the aerodynamic drag force that opposes an object’s motion through air. The power output (in watts) is the rate at which work is done to maintain the speed against this drag force. The drag force itself is a function of the drag coefficient, frontal area, and air density. As power increases, the speed at which an object can travel also increases, assuming other factors remain constant.

How to Calculate Speed from Watts?

For the drag-only reference formula, follow the steps below. In the calculator, select the solve mode, enter power or speed and total mass, set grade and review the optional assumptions before selecting Calculate. To reproduce the drag-only table, use custom Crr = 0, wind = 0, grade = 0 and drivetrain efficiency = 100%.

First, determine the power output (P) in watts.
Next, determine the drag coefficient (C_d) which is dimensionless.
Next, determine the frontal area (A) in square meters.
Next, determine the air density (ρ) in kilograms per cubic meter.
Next, gather the formula from above = S = [(2 · P) / (C_d · A · ρ)]^(1/3).
Finally, calculate the speed (S) in meters per second.
After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem :

Use the following variables as an example problem to test your knowledge.

power output (P) = 250 watts

drag coefficient (C_d) = 0.9

frontal area (A) = 0.5 m²

air density (ρ) = 1.225 kg/m³. Under the drag-only assumptions, speed is approximately 9.679965 m/s.