Enter the power, drag coefficient, frontal area, and air density into the calculator to determine the speed. This calculator helps in estimating the speed an object can achieve for a given power output (assuming aerodynamic drag power only).
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Watts to Speed Formula
The following formula is used to calculate the speed from power output (assuming all power goes into overcoming aerodynamic drag).
S = \left(\frac{2 \cdot P}{C_d \cdot A \cdot \rho}\right)^{1/3}Variables:
- S is the speed (m/s)
- P is the power output (watts)
- C_d is the drag coefficient (dimensionless)
- A is the frontal area (m²)
- ρ is the air density (kg/m³)
To calculate the speed, take the cube root of twice the power output divided by the product of the drag coefficient, frontal area, and air density.
| Power (W) | Speed (m/s) | Speed (km/h) | Speed (mph) |
|---|---|---|---|
| 50 | 6.34 | 22.83 | 14.19 |
| 75 | 7.26 | 26.14 | 16.25 |
| 100 | 7.99 | 28.77 | 17.88 |
| 125 | 8.61 | 30.98 | 19.25 |
| 150 | 9.15 | 32.93 | 20.46 |
| 175 | 9.63 | 34.67 | 21.55 |
| 200 | 10.07 | 36.25 | 22.51 |
| 225 | 10.47 | 37.70 | 23.42 |
| 250 | 10.85 | 39.05 | 24.26 |
| 275 | 11.20 | 40.33 | 25.06 |
| 300 | 11.53 | 41.49 | 25.78 |
| 325 | 11.83 | 42.60 | 26.47 |
| 350 | 12.13 | 43.67 | 27.14 |
| 375 | 12.41 | 44.67 | 27.76 |
| 400 | 12.68 | 45.66 | 28.38 |
| 450 | 13.20 | 47.50 | 29.52 |
| 500 | 13.67 | 49.20 | 30.57 |
| 600 | 14.52 | 52.29 | 32.49 |
| 700 | 15.29 | 55.04 | 34.20 |
| 800 | 15.98 | 57.54 | 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. | |||
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?
The following steps outline how to calculate the speed from power output.
- 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