Power Calculator

Mechanical power: Work/Time, Force×Velocity, Torque×RPM — with horsepower, cost estimator & power scale

Inputs

Calculation Mode

Work / Energy

Time

Power (Known)

⚡ Electricity Cost Estimator

Enter power to calculate daily cost

Results

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Enter values to calculate

Power Scale —

1µW1mW1W1kW1MW1GW10GW

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Watts (W)

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HP (mech.)

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HP (metric)

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BTU/hr

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ft·lbf/s

P = W/tWork/Time

P = F·vForce×Velocity

P = τ·ωTorque×ω

Energy Accumulated Over Time

Power Comparison Chart

Logarithmic scale — your calculated result appears as a gold bar.

Efficiency Calculator

Calculate mechanical efficiency from input and output power.

Input Power (W)

Output Power (W)

Efficiency—

Power Lost—

Force × Velocity Matrix (kW)

Appliance Energy Consumption

The row closest to your calculated power is highlighted.

Appliance	Typical Power (W)	Cost/hr at $0.13/kWh	Cost/month (4 hr/day)

Human Power Output

How to Use the Power Calculator

Choose Your Mode

Select ⚡ Work/Time for P = W/t, 🚀 Force×Velocity for P = Fv (vehicles, motors), or 🔧 Torque×RPM for P = τω (engines). Each mode also supports 3-way solve.

Enter Your Values

Type in the known quantities with appropriate units. Work supports J, kJ, kcal, Wh, kWh, BTU. Force supports N, kN, lbf, kgf. Velocity supports m/s, km/h, mph, ft/s.

See All Power Units

Results instantly appear in W, kW, HP (mech.), HP (metric), BTU/hr, and ft·lbf/s. Click the hero value to cycle units. The power scale shows where your result sits from µW to GW.

Key Terms

Power (P)

Rate of doing work or transferring energy. SI unit: Watt (W = J/s). 1 kW = 1000 W. Power tells you HOW FAST energy is used, not how much total energy.

Work (W)

Energy transferred by a force over a distance: W = F·d·cosθ. Unit: Joule (J = N·m). Unlike power, work is the total energy regardless of how long it takes.

Horsepower (HP)

Mechanical HP (US): 1 HP = 745.7 W, defined by James Watt from a horse lifting 33,000 lb-ft/min. Metric HP: 1 PS = 735.5 W. Electric motors also rated in HP.

Torque (τ)

Rotational force, measured in Newton-meters (N·m) or foot-pounds (ft·lb). Engine torque × RPM determines mechanical power output.

Angular Velocity (ω)

Rotational speed in radians per second: ω = 2πn/60 where n is RPM. The rotational equivalent of linear velocity v.

Efficiency (η)

Ratio of useful output power to input power: η = P_out/P_in. No real machine is 100% efficient — losses occur as heat, sound, or vibration.

Real-World Examples

Car Engine

200 N·m torque at 3000 RPM

P = τω = 200 × (2π×3000/60) = 200 × 314.2 = 62,832 W = 62.8 kW = 84.2 HP

A typical family car engine. Peak power often occurs at higher RPM; peak torque at lower RPM. Sports cars may have 300+ kW (400+ HP).

Cyclist

Pro cyclist sprinting: 1500 W for 5 seconds

E = P·t = 1500 × 5 = 7500 J. Sustained climbing power: ~400 W (0.54 HP)

A Tour de France cyclist can sustain 400 W for hours. Sprint power reaches 2000+ W briefly. Average person can sustain ~100–150 W.

Wind Turbine

Modern offshore turbine at full load

P = 5,000,000 W = 5 MW = 5000 kW = 6,711 HP

A single 5 MW turbine can power ~1,400 average homes. Wind turbines have ~35–45% efficiency (Betz limit: max 59.3%).

Elevator Motor

Lifting 1000 kg at 1 m/s

P = F·v = (1000 × 9.81) × 1 = 9,810 W = 9.81 kW = 13.2 HP

A 10 kW motor is sufficient. In practice, 15–20 kW is used for safety margin and acceleration. The actual energy per trip depends on height.

Understanding Mechanical Power

What is Power?

Power is the rate at which energy is transferred or work is done. The SI unit is the Watt (W = J/s), named after James Watt. If you lift a 10 kg box by 1 meter in 1 second, you do 98.1 J of work (against gravity) at a power of 98.1 W. Doing the same work in 0.5 seconds requires 196.2 W — double the power, same total energy.

Three Ways to Calculate Power

For linear motion: P = F × v (force times velocity). A car engine transmitting 5000 N of traction force at 30 m/s (108 km/h) produces 150 kW. For rotational motion: P = τ × ω = τ × (2πn/60), where τ is torque in N·m and n is RPM. A 200 N·m engine at 3000 RPM: P = 200 × 314.2 = 62.8 kW. For any system: P = W/t (total work divided by time).

Horsepower: Historical Context

James Watt needed to compare his steam engine to horses (the existing power source) to sell to miners. He measured that a horse could lift 33,000 foot-pounds per minute (or 550 ft·lbf/s), defining 1 mechanical horsepower = 745.7 W. The metric horsepower (PS, Pferdestärke) is defined as 75 kgf·m/s = 735.5 W — slightly less. European car spec sheets still commonly use PS alongside kW.

Power in Electrical Systems

Electrical power: P = V × I = I²R = V²/R (for DC; AC adds power factor). 1 kWh = 1 kilowatt × 1 hour = 3,600,000 J = 3.6 MJ. Your electricity bill is in kWh. A 1 kW device running for 1 hour uses 1 kWh of energy. At $0.13/kWh, that's $0.13. Running 24 hours/day, 365 days: 8,760 kWh/year at ~$1,139/year for a 1 kW load.

Efficiency and Real Machines

Efficiency η = P_useful / P_input × 100%. Electric motors: 85–97% efficient. Internal combustion engines: 20–40% (most fuel energy becomes heat). Steam turbines: 30–45%. Incandescent bulbs: ~5% (95% becomes heat). LED bulbs: ~30–50% efficient. The second law of thermodynamics guarantees no machine can be 100% efficient — there are always losses.

Frequently Asked Questions

What is the difference between power and energy?

Energy is the total work done (Joules or kWh). Power is the rate of energy transfer (Watts = Joules/second). A 1000 W device and a 100 W device running for 1 hour use 1 kWh and 0.1 kWh respectively — different energy for the same time. Energy = Power × Time.

How many watts is 1 horsepower?

Mechanical horsepower (US): 1 HP = 745.7 W exactly. Metric horsepower (PS/CV): 1 PS = 735.5 W. Electric horsepower: 1 ehp = 746 W exactly. Most automotive ratings use mechanical HP in the US and PS in Europe. The difference is less than 2%.

How do I calculate power from torque and RPM?

P (W) = τ (N·m) × ω (rad/s) = τ × 2πn/60, where n is RPM. Simplified: P (kW) = τ (N·m) × n (RPM) / 9549. Or in HP: HP = τ (ft·lb) × n (RPM) / 5252. Example: 300 N·m at 5000 RPM = 300 × 5000/9549 = 157 kW = 211 HP.

What is the power of a typical human?

Average human can sustain about 75–100 W (0.1 HP) for hours. Trained cyclist: 250–400 W sustained. Peak sprint: 1000–2000 W for seconds. A Tour de France climber sustains ~400 W for 40+ minutes. The average human metabolic rate at rest is ~80 W (basal metabolic rate).

How do I calculate electricity cost from power?

Cost = Power (kW) × Hours × Rate ($/kWh). Example: 2 kW heater, 6 hours/day at $0.13/kWh: Cost/day = 2 × 6 × 0.13 = $1.56. Monthly (30 days) = $46.80. US average electricity rate ≈ $0.12–0.16/kWh (2024).

What is the difference between mechanical and metric horsepower?

Mechanical HP (US): exactly 550 ft·lbf/s = 745.7 W. Metric HP (PS/CV/ch): exactly 75 kgf·m/s = 735.5 W. The difference is 10.2 W (1.4%). A car rated at 200 PS (metric) = 197.2 HP (mechanical). Most modern spec sheets show both kW and HP.

What is mechanical efficiency?

Efficiency = useful output power / total input power × 100%. A motor drawing 1000 W (input) but delivering only 850 W of mechanical work has 85% efficiency — 150 W is lost as heat. Internal combustion engines: 20–40%. Electric motors: 85–97%. Gearboxes: 95–99% per stage.

What are watts, kilowatts, and megawatts used for?

Watts: LED bulb (10 W), phone charger (20 W), laptop (45–100 W). Kilowatts: electric kettle (2 kW), hair dryer (1.5 kW), car motor (50–300 kW). Megawatts: power plant generator (500 MW), wind turbine (3–10 MW), large industrial facility (1–50 MW).

How does P = F × v work in practice?

For a vehicle: P = drag_force × velocity. At highway speed (30 m/s) with 2000 N aerodynamic drag: P = 2000 × 30 = 60,000 W = 60 kW = 80 HP required just to maintain speed (ignoring other losses). This explains why fuel efficiency drops significantly at high speed.

What is the most powerful engine ever built?

The Wärtsilä-Sulzer RTA96-C diesel engine (used in large container ships) produces about 80,080 kW (107,389 HP) at 102 RPM. The most powerful rocket engine was the F-1 (Saturn V): 690,000 kW (925,000 HP) each, five per Saturn V = 3,450,000 kW total thrust equivalent power.

What is a watt-hour vs a watt?

A Watt is power (rate). A Watt-hour (Wh) is energy = 1 W × 1 hour = 3600 J. Your electricity bill is in kWh. A phone battery is ~10–20 Wh. An electric car battery is 50–100 kWh. 1 kWh = 3,600,000 J = 3.6 MJ.

What is the Betz limit for wind turbines?

The Betz limit (59.3%) is the theoretical maximum efficiency of any wind turbine — it cannot extract more than 59.3% of the kinetic energy in the wind. This was derived by Albert Betz in 1919. Real turbines achieve 40–50% due to additional losses.

How is torque related to power and RPM?

P = τ × ω = τ × 2πn/60. So τ = P × 60 / (2πn) = P × 9549 / n (with P in kW and n in RPM, τ in N·m). High-torque engines (diesels) produce power at low RPM; high-RPM engines (sports cars) need higher RPM to achieve the same power from lower torque.

What is the unit BTU/hour used for?

BTU/hr (British Thermal Units per hour) is commonly used for heating/cooling capacity in HVAC. 1 BTU/hr = 0.293 W. A 12,000 BTU/hr air conditioner = 3,517 W = 3.5 kW of cooling capacity. 1 ton of refrigeration = 12,000 BTU/hr = 3.517 kW.

How much power does a solar panel produce?

A typical residential solar panel is 400–550 W peak (in full sunlight). Annual energy production depends on location: ~400 kWh/year in the UK, ~600 kWh/year in Germany, ~700 kWh/year in California. A 5 kW rooftop system produces ~5,000–8,000 kWh/year in sunny climates.