Power Calculator
Calculate mechanical power from work & time (P=W/t), force & velocity (P=Fv), or electrical power (P=VI). Convert between Watts, horsepower, kW, and BTU/hr.
J
s
Power (Watts)
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Power (kW) —
Power (HP) —
Power (BTU/hr) —
Extended More scenarios, charts & detailed breakdown ▾
J
s
Power (W)
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Power (HP) —
Power (kW) —
Professional Full parameters & maximum detail ▾
W
%
N·m
RPM
Pa
m³/s
Input/Output Power
Output Power (W) —
Output Power (HP) —
Output Power (kW) —
Power Loss (W) —
Rotational & Hydraulic
Rotational Power (W) —
Hydraulic Power (W) —
Unit Conversions
Output (BTU/hr) —
Output (ft·lb/s) —
How to Use This Calculator
- Select your calculation mode: Work & Time, Force & Velocity, or Electrical.
- Enter the required values.
- Results show power in Watts, HP, kW, and BTU/hr simultaneously.
- Use the Professional tab for efficiency factor, rotational power, and hydraulic power.
Formula
P = W/t (Work J ÷ Time s = Power W)
P = F × v (Force N × Velocity m/s)
P = V × I (Voltage × Current)
P = τ × ω (Torque × Angular velocity)
1 HP = 745.7 W | 1 kW = 1000 W
Example
Example: 5,000 J of work in 10 seconds. P = 5,000 ÷ 10 = 500 W = 0.671 HP = 0.5 kW.
Frequently Asked Questions
- Power (P) is the rate of doing work: P = Work (J) ÷ Time (s). The SI unit is the Watt (W), where 1 W = 1 J/s. Other forms of the power formula include: P = Force (N) × Velocity (m/s) for mechanical power, P = Voltage (V) × Current (A) for electrical power, P = Torque (N·m) × Angular Velocity (rad/s) for rotational power. Example: lifting a 100 N weight 2 meters in 4 seconds: P = (100 × 2) ÷ 4 = 50 W. This calculator accepts all three mechanical forms and the electrical form.
- Mechanical horsepower (HP) = Watts ÷ 745.7. For example, 1,000 W ÷ 745.7 = 1.341 HP. To convert the other way: Watts = HP × 745.7. Common conversions: 100 W = 0.134 HP, 1 kW = 1.341 HP, 10 HP = 7,457 W = 7.46 kW. Note there are different definitions: mechanical horsepower (745.7 W), metric horsepower (735.5 W), and electrical horsepower (746 W exactly). Car engines are typically rated in metric horsepower in Europe and mechanical horsepower in the US. This calculator uses the standard mechanical HP definition.
- Kilowatts (kW) = Watts ÷ 1,000. One kilowatt equals exactly 1,000 watts. 1 kW = 1.341 HP. To convert kW to watts, multiply by 1,000. For context: a standard LED light bulb uses 9–10 W (0.009–0.01 kW), a microwave uses 1,000–1,500 W (1–1.5 kW), a central air conditioner uses 3,000–5,000 W (3–5 kW), and a typical US home uses an average of about 1.2 kW continuously (about 10,500 kWh per year). Electric vehicle motors typically range from 50–300 kW (67–400 HP).
- Rotational (mechanical) power is calculated as P = τ × ω, where τ (tau) is torque in Newton-meters (N·m) and ω (omega) is angular velocity in radians per second (rad/s). Convert RPM to rad/s: ω = RPM × 2π ÷ 60. For example, an engine producing 200 N·m of torque at 3,000 RPM: ω = 3000 × 2π ÷ 60 = 314.16 rad/s. P = 200 × 314.16 = 62,832 W = 62.8 kW = 84.3 HP. This is why engine power ratings are always given at a specific RPM — the same torque at higher RPM produces more power.
- Hydraulic power is the power transmitted by pressurized fluid: P = Pressure (Pa) × Flow Rate (m³/s). Since 1 Pa × 1 m³/s = 1 W (watt). In practical units: P (kW) = Pressure (bar) × Flow (L/min) ÷ 600. For example, a hydraulic system at 200 bar with 10 L/min flow: P = 200 × 10 ÷ 600 = 3.33 kW. In US units: HP = Pressure (psi) × Flow (GPM) ÷ 1,714. Hydraulic power is used in construction equipment, industrial presses, and aircraft landing gear. The efficiency factor (typically 80–90%) must be applied to get actual shaft power from the motor.