BYTETOOLS

Torque Calculator

Work out torque, force, lever arm or angle from τ = r·F·sin θ in N·m, lb·ft, lb·in or kgf·m, and turn torque plus rpm into shaft power.

30 N·m
Torque

τ = r · F · sin θ

  • τ = 0.3 m × 100 N × sin 90° = 30 N·m
  • 30 N·m = 22.1269 lb·ft = 265.5224 lb·in = 3.0591 kgf·m
  • Perpendicular force component F⊥ = F · sin θ = 100 N
  • Effective (perpendicular) lever arm r⊥ = r · sin θ = 0.3 m

Rotational power — P = τ · ω

104.72 rad/s
Angular velocity ω
3,141.59 W
Shaft power
3.1416 kW
In kilowatts
4.2129 hp
In horsepower

ω = 2πN ÷ 60 converts revolutions per minute into radians per second, then P = τω gives the mechanical power a shaft delivers at that torque and speed.

Worked example — tightening a bolt with a 300 mm spanner pulled at 100 N perpendicular to the handle gives τ = 0.3 × 100 × sin 90° = 30 N·m, which is 22.13 lb·ft. Only the component of force perpendicular to the arm turns the bolt; pulling along the handle does nothing. Published bolt-torque specifications assume a particular thread condition and lubrication, so always follow the manufacturer's figure rather than a general calculation.

What is the Torque Calculator?

Torque is the turning effect of a force: τ = r·F·sin θ, where r is the distance from the pivot, F is the force and θ is the angle between them. A 100 N force on a 0.3 m spanner, pulled at right angles, gives 30 N·m.

  • Solves τ = r·F·sin θ for torque, force, lever arm or angle
  • Nine torque units including N·m, lb·ft, lb·in, oz·in and kgf·m
  • Shows the perpendicular force component and effective lever arm
  • Rotational power panel converts rpm to rad/s and gives P = τω
  • Clear errors when a sine above 1 makes the requested angle impossible
  • Runs entirely in the browser, with nothing sent to a server

How to use the Torque Calculator

  1. 1

    Choose what to solve for: torque, force, lever arm or the angle between them.

  2. 2

    Enter the known values and pick their units — force in N, kN or lbf, lever arm in mm, cm, m, in or ft.

  3. 3

    Set the angle θ between the lever arm and the force; 90° is the perpendicular, most effective case.

  4. 4

    Read the torque with its conversions to lb·ft, lb·in and kgf·m in the working panel.

  5. 5

    Enter a rotation speed in rpm in the power panel to see the equivalent shaft power in W, kW and hp.

About the Torque Calculator

The ByteTools Torque Calculator solves τ = r·F·sin θ for whichever quantity you do not know — the torque itself, the force you have to apply, the lever arm you need, or the angle between them. It prints the rearranged formula with the answer and also reports the perpendicular force component and the effective lever arm, so it is clear why the angle matters so much.

Torque can be entered or displayed in newton-metres, newton-centimetres, kilonewton-metres, pound-feet, pound-inches, ounce-inches or kilogram-force metres, which covers physics homework, bicycle and car workshop specifications, and small-motor datasheets alike. A separate panel takes a rotation speed in rpm, converts it with ω = 2πN ÷ 60, and reports the shaft power τω in watts, kilowatts and horsepower.

All the arithmetic happens in your browser in plain JavaScript. No values are uploaded to a server and nothing is stored between visits, so results update instantly as you type and the tool stays available offline once the page has loaded.

Frequently asked questions

How do you calculate torque?

Multiply the distance from the pivot by the force and by the sine of the angle between them: τ = r·F·sin θ. Pulling a 300 mm spanner with 100 N at right angles gives 0.3 × 100 × sin 90° = 30 N·m, which is 22.13 lb·ft.

How many newton-metres is one pound-foot?

One pound-foot equals 1.3558 newton-metres, so a 100 lb·ft specification is about 135.6 N·m. The calculator converts between N·m, lb·ft, lb·in and kgf·m automatically, so you can enter a figure in the units your torque wrench uses.

Why does a longer spanner make a bolt easier to turn?

Torque grows in proportion to the lever arm, so doubling the length of the handle halves the force you need for the same torque. That is the whole idea behind breaker bars and long-handled wrenches on seized fasteners.

How do you convert torque and rpm into horsepower?

First convert rpm to radians per second with ω = 2πN ÷ 60, then multiply by the torque: P = τω gives watts. Divide by 745.7 for horsepower. The power panel in this tool does both steps for you.

Can I use this for bolt tightening specifications?

It gives the correct physics for the force and lever arm you enter, but published bolt torques assume a particular thread condition, lubrication and clamp load. Always follow the manufacturer's figure and torque wrench procedure rather than a general calculation.

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