🎯 Solve for:
Enter work or energy.
Enter time.
Enter power.
🎯 Solve for:
Enter force.
Enter velocity.
Enter power.
Power
—
💡
ℹ️ P = W/t gives average power over a time period. P = F×v gives instantaneous power when force and velocity are parallel. For non-parallel cases: P = F×v×cos(θ).
Was this calculator helpful?
Sources & Methodology
Power formulas and unit conversions per NIST SI definitions and Serway & Jewett Physics.
Serway & Jewett — Physics for Scientists and Engineers, 10th Ed.
Standard university reference for mechanical power, P = W/t, P = Fv, and energy conversion.
NIST — SI Unit Definitions: Watt
1 W = 1 J/s = 1 kg·m²/s³. Horsepower: 1 hp = 745.699872 W. physics.nist.gov
Halliday, Resnick & Krane — Physics, 5th Ed.
Treatment of power, work, and mechanical energy in classical mechanics.
P = W / t [watts = J/s]
P = F × v [when force parallel to velocity]
1 hp = 745.7 W • 1 kW = 1000 W
Energy = Power × Time: E = P × t
P = F × v [when force parallel to velocity]
1 hp = 745.7 W • 1 kW = 1000 W
Energy = Power × Time: E = P × t
P = W / t P = F × v
Example 1: 1000 J of work done in 10 s: P = 1000/10 = 100 W
Example 2: 2000 N force at 30 m/s: P = 2000 × 30 = 60,000 W = 60 kW = 80.5 hp
Example 2: 2000 N force at 30 m/s: P = 2000 × 30 = 60,000 W = 60 kW = 80.5 hp
Last reviewed: April 2026
How Is Mechanical Power Calculated?
Power is the rate at which work is done or energy is transferred. The fundamental formula is P = W/t — work (joules) divided by time (seconds) gives power in watts. For a constant force applied to a moving object, power can also be expressed as P = F × v (force times velocity).
The SI unit of power is the watt (W), named after James Watt. One watt equals one joule per second. The horsepower (hp) unit derives from James Watt's comparison of steam engine output to horse pulling capacity: 1 hp = 550 ft·lb/s = 745.7 W.
Power Conversion Reference
| Unit | Watts (W) | Notes |
|---|---|---|
| 1 Watt | 1 W | 1 J/s = SI base unit |
| 1 Kilowatt | 1,000 W | Typical household appliances |
| 1 Horsepower (hp) | 745.7 W | US mechanical horsepower |
| 1 Metric HP (PS) | 735.5 W | European car engine ratings |
| 1 BTU/hr | 0.2931 W | HVAC and heating |
| 1 Megawatt | 1,000,000 W | Power plants, large industry |
💡 Real-World Power Examples: Human at rest ~80 W. Cycling (recreational) ~100-200 W. Elite cyclist (sustained) ~400 W. Car cruising ~15-25 kW. Car engine max ~100-300 kW. A single horsepower is 745.7 W — a human can sustain only about 1/4 hp (roughly 200 W) for extended periods.
Frequently Asked Questions
P = W/t (work/time) or P = F×v (force×velocity). SI unit: watt (W) = J/s. Also: P = ΔE/t for any energy transfer rate.
1 watt = 1 joule per second = 1 kg·m²/s³. Named after James Watt. 1 kW = 1000 W. 1 MW = 1,000,000 W.
hp = W / 745.7. Example: 60,000 W = 60,000/745.7 = 80.5 hp. To convert hp to W: W = hp × 745.7.
Energy (J) = total work done. Power (W) = rate of energy transfer = E/t. A 100 W bulb for 1 hr uses 360,000 J = 0.1 kWh of energy.
P = F×v is the instantaneous power delivered by force F to an object at velocity v (when parallel). Example: 2000 N thrust at 30 m/s: P = 60,000 W = 60 kW.
1 mechanical hp = 745.699872 W. 1 metric hp (PS/CV) = 735.499 W. Mechanical hp used in US; metric hp used in Europe.
Average P = total work / total time. Instantaneous P = dW/dt = F×v at a specific moment. For constant force and velocity they are equal.
P = F×v (parallel). Example: cyclist 150 N at 8 m/s: P = 1200 W = 1.2 kW. If angle θ: P = F×v×cos(θ).
At rest: ~80-100 W. Cycling sustained: 300-400 W. Sprint peak: 1000-2000 W. Average US household uses ~1.2 kW continuously.
Efficiency = (useful output power / input power) × 100%. Car engine: ~25-35%. Electric motor: ~90-95%. No machine is 100% efficient due to friction and heat losses.
Related Calculators
Popular Calculators
AGI Calculator
Education
Ohms Law Calculator
Education
Course Pricing Calculator
Education
Stripe Fee Calculator
Finance
Pain & Suffering
Legal
TDEE Calculator
Health
Roofing Calculator
Construction
GPA Calculator
Education
Mortgage Refinance
Finance
CPM Calculator
Marketing
Markup Calculator
Finance
Angle Conversion Calculator
Education