What is the SI unit of power and how is it defined?

The SI unit of power is the watt (W), named after James Watt. One watt equals one joule of energy transferred per second (1 W = 1 J/s). Larger multiples — kilowatt (kW = 1 000 W), megawatt (MW = 1 000 000 W) — are common in engineering. The imperial unit horsepower (1 hp = 745.7 W) is still widely used for engines and motors.

How does the calculator handle the formula P equals W divided by t?

P = W/t is the most fundamental definition of power: divide the total energy (work done, in joules) by the elapsed time (in seconds) to get the average power in watts. The calculator also rearranges the formula so you can solve for energy (W = P × t) or time (t = W/P). It converts the result to kWh, kcal, and hours automatically.

When do I use P equals F times v versus P equals W divided by t?

P = Fv is the instantaneous mechanical power for an object experiencing a constant force F (newtons) moving at velocity v (m/s). It is most useful for engines, vehicles, and conveyor belts where you know the thrust force and speed rather than the total energy over a period. P = W/t is better when you know the total energy released or consumed over a measured time interval.

What is P equals tau times omega and when is it used?

P = τω is the rotational analogue of P = Fv. Torque τ (in N·m) is the rotational equivalent of force, and angular velocity ω (in rad/s) is the rotational equivalent of linear velocity. Engine power is almost always measured this way: a dynamometer measures torque at a given rpm, and P = τω gives shaft power. The calculator accepts rpm directly and converts it to rad/s internally.

Which electrical power formula should I use — P = VI, P = I²R, or P = V²/R?

All three are equivalent via Ohm's law (V = IR), but each is convenient when certain quantities are known. Use P = VI when you have both voltage and current readings (e.g. a multimeter measurement). Use P = I²R (Joule heating) when current and resistance are known — common for resistors, heating elements, and cable sizing. Use P = V²/R when voltage and resistance are known — typical for load calculations at a fixed supply voltage.

What does the inverse-square law mode calculate?

The radiation intensity mode implements the inverse-square law: I = P / (4πr²). For a point source radiating isotropically (equally in all directions), intensity falls off with the square of distance. Doubling the distance from a source reduces intensity to one-quarter. This applies to sound, light, radio waves, and radiation. The calculator lets you solve for total power P, intensity I at a given distance r, or the distance r at which a given intensity is reached.

Power Physics Calculator

Power is the rate at which energy is transferred or converted — and a single definition, P = W/t (power equals energy divided by time), branches into a rich family of formulas depending on the physical context. A spinning shaft obeys P = τω; a resistor dissipates P = I²R; a pump delivers P = ρgQh; a light bulb radiates P = 4πr²I at distance r. This calculator brings all of those formulas into one tool, lets you solve for any variable, and shows every substitution step in plain numbers.

Formulas covered

The calculator covers ten distinct power relationships:

P = W/t — energy divided by time (the fundamental definition; works in any domain)
P = Fv — force times velocity (mechanical, translational motion)
P = τω — torque times angular velocity (rotational machines, engines)
P = VI — voltage times current (electrical, Joule’s First Law)
P = I²R — current-squared times resistance (Joule heating, resistive dissipation)
P = V²/R — voltage-squared divided by resistance (load at fixed supply voltage)
P = ρgQh — hydraulic power (fluid density × gravitational acceleration × flow rate × head)
P = |ΔKE_rot|/t — average power to spin up or brake a rotating body (½Iω²)
P = mgh/t — power to raise a mass against gravity (gravitational potential energy rate)
I = P/(4πr²) — radiation intensity from a point source (inverse-square law)

Every mode is bidirectional: if you know the output power and one other variable, you can solve backward for the missing input.

How it works

Pick a formula from the dropdown, choose what to solve for within that formula, enter the known values, and the result appears in engineering notation (e.g. 15.7 kW rather than 15700 W). Unit selectors sit beside each input so you can enter rpm instead of rad/s, horsepower instead of watts, or miles per hour instead of m/s — the calculator converts to SI internally, computes, and reports back in watts (with additional equivalent values such as hp and kWh shown in the working).

The step-by-step working panel shows every substitution: the formula, each numerical substitution with units, and the final value. Hit “Copy” to paste the full working chain into a report, homework answer, or engineering note.

Constants used: g = 9.80665 m/s², 1 hp = 745.69987 W.

Worked example — engine torque to shaft power

A car engine produces 150 N·m of torque at 3 500 rpm. What is the shaft power?

Convert rpm to rad/s: ω = 3 500 × π/30 = 366.5 rad/s
Apply P = τω: P = 150 × 366.5 = 54 974 W
Convert: 54 974 W ÷ 745.7 = 73.7 hp

Select “P = τω”, enter 150 N·m and 3500 rpm, and the calculator shows the same result with all steps.

Formula reference table

Formula	Solve for	Domain
P = W ÷ t	P, W, or t	Universal
P = F × v	P, F, or v	Translational mechanics
P = τ × ω	P, τ, or ω	Rotational mechanics
P = V × I	P, V, or I	Electrical
P = I² × R	P, I, or R	Electrical (Joule heating)
P = V² ÷ R	P, V, or R	Electrical (fixed-voltage load)
P = ρgQh	P (hydraulic + shaft)	Hydraulics / pumps
P =	ΔKE_rot	÷ t
P = mgh ÷ t	P	Gravitational lifting
I = P ÷ (4πr²)	P, I, or r	Radiation / acoustics

All calculations run entirely in your browser — nothing is uploaded or stored.