# Mechanical Calculator

All-in-one mechanical calculator. Compute force, work, power, torque, weight, or mechanical advantage in SI and imperial. Use the formulas F = ma, W = Fd, P = W/t, tau = Fr.

## What this calculates

A mechanical calculator runs the core equations of classical mechanics in one place. Pick a mode (force, work, power, torque, weight, mechanical advantage), enter the known quantities, and the calculator returns the result in both SI and imperial units. Handy for homework, quick shop-floor checks, and anyone who does not want to open six different tools to size a lever, a rope, or a motor.

## Inputs

- **Mechanical Quantity** — options: Force (F = m x a), Work (W = F x d), Power (P = W / t), Torque (t = F x r), Mechanical advantage (MA = load / effort), Weight (w = m x g) — Pick the mechanical quantity you want to calculate. Each mode changes which inputs apply.
- **Mass** (kg) — min 0 — Used by force, weight, and momentum-style modes.
- **Acceleration** (m/s^2) — min 0 — Acceleration in m/s^2. Default 9.81 is Earth gravity.
- **Force** (N) — min 0 — Used by work, power, torque, and mechanical advantage modes.
- **Distance / Radius** (m) — min 0 — Distance for work, or the radius (lever arm) for torque. SI is metres.
- **Time** (s) — min 0 — Time elapsed, used in power mode (P = W / t).
- **Load Force** (N) — min 0 — Load the machine has to lift or move. Mechanical advantage mode only.
- **Effort Force** (N) — min 0 — Force applied at the input of the machine. Mechanical advantage mode only.

## Outputs

- **Result** — formatted as text — Primary result in SI and imperial where applicable.
- **Value (SI)** — Numeric result in SI units.
- **Value (Imperial)** — Numeric result in imperial units, where applicable.
- **SI Unit** — formatted as text — SI unit label for the computed value.
- **Imperial Unit** — formatted as text — Imperial unit label for the computed value.

## Details

The six core mechanical calculator modes

This mechanical calculator covers the classical Newtonian equations that cover 90 percent of practical problems:

  - Force (F = m x a). Newton's second law. A 10 kg object accelerating at 9.81 m/s^2 feels 98.1 N of force, roughly the weight of a full 2.5 gallon bucket of water on Earth.

  - Weight (w = m x g). The gravitational force on a mass. Weight is a force (newtons), not a mass. A 10 kg object weighs 98.1 N on Earth, 16.2 N on the Moon, and 371 N on Jupiter.

  - Work (W = F x d). The energy transferred by a force moving an object over a distance. A 100 N force applied over 5 m does 500 J of work. In imperial, 500 J equals 368.8 ft-lbf.

  - Power (P = W / t). The rate of doing work. 500 J in 10 s is 50 W, or about 0.067 horsepower. A modern electric kettle pulls roughly 1800 W, a marathon-running human produces about 250 W average.

  - Torque (tau = F x r). Rotational force. A 100 N push at the end of a 0.5 m wrench produces 50 N.m (about 37 ft-lbf) of torque, enough to seat a typical wheel stud.

  - Mechanical advantage (MA = load / effort). How much a simple machine multiplies force. A pulley system lifting a 500 N load with 100 N effort has MA = 5. A car jack is typically MA = 50 or higher.

Worked mechanical calculator examples

  
    ProblemFormulaResult
  
  
    Force on a 10 kg mass at 9.81 m/s^2F = 10 x 9.8198.1 N (22.05 lbf)
    Work to lift 20 kg by 2 mW = (20 x 9.81) x 2392.4 J (289.4 ft-lbf)
    Power to climb 3 m of stairs in 4 s (80 kg person)P = (80 x 9.81 x 3) / 4588.6 W (0.789 hp)
    Torque from 50 N at 0.3 mtau = 50 x 0.315 N.m (11.06 ft-lbf)
    MA of a 4:1 pulleyMA = 400 / 1004:1
  

Mechanical calculator for homework and shop work

If you are learning mechanics for the first time, this mechanical calculator is a good way to double-check hand calculations. Do the algebra yourself, then plug the numbers in here and make sure the answer matches. If you are a machinist or mechanic, the torque and power modes are fastest: enter force and lever arm to size a bolt, or enter work and time to know whether a motor is strong enough.

For ratings and motor sizing, remember the SI-to-imperial conversions this calculator applies: 1 N = 0.2248 lbf, 1 N.m = 0.7376 ft-lbf, 1 W = 1/745.7 hp, 1 J = 0.7376 ft-lbf. The calculator returns both systems so you never have to do the conversion by hand.

## Frequently Asked Questions

**Q: What is a mechanical calculator?**

A: In this context, a mechanical calculator is a physics tool that handles the classical equations of Newtonian mechanics: F = ma (force), W = Fd (work), P = W/t (power), tau = Fr (torque), w = mg (weight), and MA = load / effort (mechanical advantage). Historically a mechanical calculator meant a gear-driven adding machine, but today the phrase usually refers to a mechanics calculator like this one.

**Q: What is the formula for force?**

A: Newton's second law: F = m x a, force equals mass times acceleration. Mass in kilograms, acceleration in m/s^2, gives force in newtons. A 10 kg object accelerated at 2 m/s^2 feels 20 N of force. For weight specifically, acceleration is the local gravitational acceleration, so weight = mass x g (9.80665 m/s^2 on Earth).

**Q: What is work in physics?**

A: Work is energy transferred when a force moves an object over a distance in the direction of the force: W = F x d. A 100 N push moving an object 5 m does 500 joules of work. Work is a scalar (no direction). If the force is perpendicular to the motion, work equals zero, which is why a satellite orbiting Earth does no work against gravity.

**Q: How do I calculate power from force and velocity?**

A: Two equivalent forms. From work and time: P = W / t. From force and velocity: P = F x v. A 500 N drag force on a car travelling 20 m/s requires 10,000 W (10 kW, about 13.4 hp) of engine power just to maintain speed. This mechanical calculator uses P = W / t, but the two forms give the same answer when v = d / t.

**Q: What is mechanical advantage?**

A: Mechanical advantage is the factor by which a simple machine multiplies force. MA = load / effort. A lever with a 1 m effort arm and a 0.2 m load arm has MA = 5: a 100 N effort lifts 500 N. Pulleys, gears, screws, and inclined planes all work the same way. In a frictionless machine MA also equals the ratio of input distance to output distance, so a 5:1 machine moves the effort five times further than the load.

**Q: Does this mechanical calculator handle imperial units?**

A: Yes. Mass accepts kg or lb, force accepts newtons or lbf, distance accepts metres or feet. The output shows both SI and imperial units side by side. Internally the calculator uses SI, then converts: 1 N = 0.2248 lbf, 1 N.m = 0.7376 ft-lbf, 1 J = 0.7376 ft-lbf, 1 W = 1/745.7 hp.

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Source: https://vastcalc.com/calculators/physics/mechanical
Category: Physics
Last updated: 2026-04-08