Power Calculator

Power equals work divided by time

Solution

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Power from Work

Power is the rate at which work is done. Given the total work (or energy) and the time taken, this equation yields power in watts. One watt equals one joule per second.

P = W / t

Power from Force and Velocity

When a constant force moves an object at a constant velocity, the power delivered equals force times velocity. Useful for engines, motors, and conveyor systems.

P = F × v

Electrical Power

Electrical power equals voltage multiplied by current. This is the fundamental equation for sizing circuits, selecting wire gauges, and calculating energy consumption.

P = V × I

Power from Displacement

When force acts over a displacement in a given time, power equals force times displacement divided by time. This combines the work and rate concepts into one formula.

P = F × d / t

How It Works

Power measures how fast energy is transferred or work is done. This calculator supports four formulas: P = W/t (work over time), P = F·v (force times velocity), P = V·I (voltage times current), and P = Fd/t (force times displacement over time). The SI unit is the watt (W), equal to one joule per second.

Example Problem

An engine exerts 200 N of force on a car moving at 15 m/s. What power does it deliver?

  1. Identify the knowns. Force F = 200 N (the constant driving force the engine applies to the car) and velocity v = 15 m/s (the steady forward speed of the car).
  2. Identify what we're solving for. We want the mechanical power P the engine delivers to the car, in watts (W).
  3. Write the force-velocity power equation: P = F × v. This form applies whenever a constant force moves an object at constant velocity.
  4. Substitute the known values: P = 200 N × 15 m/s.
  5. Simplify the arithmetic: P = 3,000 N·m/s, and 1 N·m/s = 1 W, so the result carries units of watts.
  6. State the final result with units: **Power P = 3,000 W = 3 kW** — equivalent to roughly 4.0 mechanical horsepower (3,000 ÷ 745.7).

In electrical terms, a 120 V outlet supplying 10 A delivers 120 × 10 = 1,200 W.

When to Use Each Variable

  • Solve for Power (Work) — when you know the total work or energy and the time taken, e.g., calculating the power output of an engine from dynamometer data.
  • Solve for Power (Force × Velocity) — when a constant force moves an object at a steady speed, e.g., determining motor power for a conveyor belt.
  • Solve for Electrical Power — when you know voltage and current, e.g., sizing a circuit breaker or calculating appliance energy consumption.
  • Solve for Power (Displacement) — when force acts over a distance in a given time, e.g., calculating the power needed to push a piston a certain stroke length.

Key Concepts

Power is the rate of doing work or transferring energy, measured in watts (1 W = 1 J/s). It can be expressed as work over time (P = W/t), force times velocity (P = Fv), voltage times current (P = VI), or force times displacement over time (P = Fd/t). These are all equivalent — they just use different known quantities.

Applications

  • Electrical systems: sizing circuit breakers and wiring based on P = VI for appliance loads
  • Automotive engineering: calculating engine power output from dynamometer force and roller speed measurements
  • Manufacturing: determining motor power requirements for conveyor belts moving loads at constant speed
  • Fitness science: measuring human power output during cycling or weightlifting exercises

Common Mistakes

  • Confusing power and energy — power is a rate (joules per second), energy is the total (joules); running a 100 W bulb for 10 hours uses 1,000 Wh of energy
  • Forgetting efficiency losses in P = VI — the electrical power input is always higher than mechanical output due to motor and friction losses
  • Using inconsistent units — mixing feet with newtons or pounds with meters gives nonsensical results; verify all values are in the same unit system before calculating

Frequently Asked Questions

What is the difference between power and energy?

Energy is the total amount of work done or heat transferred (measured in joules). Power is the rate at which that energy is used (joules per second, or watts). A 100 W bulb uses 100 J every second.

How do you convert watts to horsepower?

One mechanical horsepower equals about 745.7 W. Divide watts by 745.7 to get HP. For example, 3,000 W ÷ 745.7 ≈ 4.02 HP.

What is a kilowatt-hour?

A kilowatt-hour (kWh) is a unit of energy, not power. It equals the energy consumed by a 1 kW device running for one hour: 1 kWh = 3.6 MJ.

Which power formula should I use when?

Use P = W/t when you know total energy and the time it took. Use P = F·v for steady-state mechanical systems like motors at cruise. Use P = V·I for electrical circuits. Use P = F·d/t when force, distance, and time are all given separately rather than as work or velocity.

Is mechanical horsepower the same as electrical horsepower?

Close but not identical. Mechanical horsepower equals 745.7 W, electrical horsepower is defined exactly as 746 W, and metric horsepower (PS, used in European auto specs) is 735.5 W. The differences are small (~1%) but matter on nameplate ratings.

Why does the same engine output less power at high altitude?

An internal-combustion engine produces power by burning fuel with oxygen. Thinner air at altitude means less oxygen per intake stroke, so the engine produces less work per cycle and less power overall. Turbocharging and forced induction compensate by pre-compressing the intake air back to sea-level density.

How is power related to torque on a rotating shaft?

For rotational systems, P = τ·ω, where τ is torque (N·m) and ω is angular velocity (rad/s). An engine spec of "200 N·m at 5000 rpm" gives P = 200 × (5000 × 2π/60) ≈ 105 kW (≈ 140 hp). The linear and rotational power equations are equivalent forms.

Reference: Lindeburg, Michael R. 1992. Engineer In Training Reference Manual. Professional Publication, Inc. 8th Edition.

Worked Examples

Automotive Engineering

How much power does a Tesla Model 3 burn just to push air at highway speed?

At 100 km/h (~27.78 m/s) cruising, a Tesla Model 3 experiences about F = 350 N of aerodynamic drag (Cd × frontal area × ½ρv² works out to roughly that on this car). At steady speed all of the motor's drive force is fighting drag, so P = F × v gives the cruising power draw.

  • Knowns: F = 350 N (highway drag), v = 27.78 m/s
  • P = F × v
  • P = 350 × 27.78

P ≈ 9,723 W (~9.7 kW, about 13 HP)

That is why electric cars get such good highway range — 9.7 kW at 100 km/h means a 75 kWh battery has ~7.7 hours, or about 770 km of pure-drag range before rolling resistance and electronics losses. Drag scales with v², so 130 km/h cuts that range almost in half.

Electrical Engineering

How much power does a 20 V, 4.5 A USB-C laptop charger deliver?

USB Power Delivery negotiates a fixed voltage and current pair — common laptop profiles include 20 V at 3 A (60 W) or 20 V at 4.5 A (90 W). For a 20 V × 4.5 A profile, P = V × I gives the delivered electrical power.

  • Knowns: V = 20 V, I = 4.5 A
  • P = V × I
  • P = 20 × 4.5

P = 90 W

Real USB-PD chargers run at 85–92% efficiency, so the wall-socket draw is closer to 100 W. The newer USB-PD 3.1 EPR spec pushes this up to 240 W via 48 V at 5 A — pushing voltage higher (instead of current) keeps cable losses I²R in check at higher power.

Manufacturing

What average power does a hydraulic forging press deliver per stroke?

A hydraulic forging press compresses a hot steel billet, doing W = 100,000 J (100 kJ) of mechanical work during a single forming stroke that takes Δt = 4 s from contact to bottom of stroke. Average power across the stroke is P = W / t.

  • Knowns: W = 100,000 J, t = 4 s
  • P = W / t
  • P = 100,000 / 4

P = 25,000 W (25 kW)

Average power across the cycle is far lower because the press is idle most of the duty cycle while the operator loads the next billet. The hydraulic accumulator stores energy slowly between strokes and releases it quickly during the forming stroke, which is why peak instantaneous power dwarfs the steady-state motor rating.

Power Formulas

Power is the rate of doing work or transferring energy. Four equivalent equations describe it depending on which quantities you measure:

P = W / tPower from work and time
P = F × vPower from force and velocity
P = V × IElectrical power
P = F × d / tPower from force, displacement, and time

Where:

  • P — power, in watts (W), where 1 W = 1 J/s
  • W — work or energy transferred, in joules (J)
  • t — time over which the work occurred, in seconds (s)
  • F — applied force, in newtons (N)
  • v — velocity in the direction of the force, in m/s
  • V — electrical potential difference, in volts (V)
  • I — electrical current, in amperes (A)
  • d — displacement, in meters (m)

All four forms are equivalent — they just use different known quantities. P = F·v is the steady-state version of P = F·d/t. Mechanical horsepower is 745.7 W; metric horsepower (PS) is 735.5 W. For rotational systems, the analogous equation is P = τ·ω, with torque in N·m and angular velocity in rad/s.

Reference: Lindeburg, Michael R. 1992. Engineer In Training Reference Manual. Professional Publication, Inc. 8th Edition.

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