Torque Calculator — Force, Lever Arm & Power/RPM Solver

Calculate torque from force and lever arm at any angle, or solve for torque, power, or RPM given any two values. Metric and imperial units.

July 14, 2026

90% found this helpful

Reference Values

Last verified: Jul 11, 2026

Category	Range	What It Means	Status
Torque Formula (θ = 90°, perpendicular force) ★	τ = F × r	The common case: force applied perpendicular to the lever arm. This is what most wrench, pedal, and lug-nut torque specs assume by default.	★ Best
Torque Formula (general, any angle)	τ = F × r × sin(θ)	Full formula for force applied at any angle θ to the lever arm. Reduces to F × r when θ = 90° since sin(90°) = 1, and to zero when the force is applied along the arm's length (θ = 0°).	Good
Power from Torque + RPM (metric)	P (kW) = T (N·m) × RPM ÷ 9549	Direct formula for shaft power when torque is in newton-meters and speed is in RPM. Derived from P = τ × ω, where ω = RPM × 2π/60.	Good
Power from Torque + RPM (imperial)	P (HP) = T (lb-ft) × RPM ÷ 5252	Direct formula for horsepower when torque is in pound-feet and speed is in RPM. The constant 5252 comes from 33,000 ft-lb/min per HP divided by 2π.	Good
Angular velocity	ω (rad/s) = RPM × 2π ÷ 60	Converts rotational speed in RPM to angular velocity in radians per second, the unit power-torque physics equations use directly (P = τ × ω).	Okay
N·m to lb-ft	1 N·m = 0.737562 lb-ft	Standard SI-to-imperial torque conversion factor.	Okay
lb-ft to N·m	1 lb-ft = 1.355818 N·m	Standard imperial-to-SI torque conversion factor, the inverse of the N·m to lb-ft factor.	Okay
HP to kW	1 HP = 0.745700 kW	Mechanical horsepower to kilowatts, used to cross-check power results between imperial and metric torque-power-RPM calculations.	Okay

Source: Standard engineering statics/dynamics torque formula (τ = F × r × sinθ) and power-torque-speed relationship (P = τω), as documented in Testbook's 'Relation Between Torque and Power' reference and Physics of the Universe's torque calculator methodology. Unit conversion factors per NIST Special Publication 811.

Worked Examples

Lug Wrench, Perpendicular Force

Force: 150 N
Lever Arm: 0.45 m
Angle: 90°

67.5 N·m

τ = F × r × sin(θ) = 150 × 0.45 × sin(90°) = 150 × 0.45 × 1 = 67.5 N·m. Perpendicular force (θ = 90°) is the standard case most torque wrench specs assume.

Breaker Bar Pulled at an Angle

Force: 100 lb
Lever Arm: 2 ft
Angle: 60°

173.21 lb-ft

τ = F × r × sin(θ) = 100 × 2 × sin(60°) = 200 × 0.86603 = 173.21 lb-ft. Pulling at an angle instead of perpendicular loses about 13% of the torque compared to a 90° pull with the same force.

Engine Dyno: Torque + RPM → Power (Metric)

Torque: 200 N·m
RPM: 3000
Solve for: Power

62.83 kW

P (kW) = T (N·m) × RPM ÷ 9549 = 200 × 3000 ÷ 9549 = 600,000 ÷ 9549 = 62.83 kW.

Motor Spec Sheet: Power + RPM → Torque (Imperial)

Power: 200 HP
RPM: 4000
Solve for: Torque

262.6 lb-ft

T (lb-ft) = P (HP) × 5252 ÷ RPM = 200 × 5252 ÷ 4000 = 1,050,400 ÷ 4000 = 262.6 lb-ft.

Generator Sizing: Power + Torque → RPM (Metric)

Power: 50 kW
Torque: 150 N·m
Solve for: RPM

3183 RPM

RPM = P (kW) × 9549 ÷ T (N·m) = 50 × 9549 ÷ 150 = 477,450 ÷ 150 = 3183 RPM.

How to Use This Calculator

1

Choose a calculation mode

'Basic Torque' finds torque from force, lever arm, and angle. 'Torque, Power & RPM Solver' finds any one of those three values given the other two.
2

Basic mode: enter force, lever arm, and angle

Angle defaults to 90° for a perpendicular push or pull — the standard assumption for wrench and bolt-torque specs. Lower the angle to see how much torque you lose pulling at a shallower angle.
3

Solver mode: pick what to solve for

Choose Torque, Power, or RPM as the unknown, then enter the other two values. The chosen field is grayed out and fills in automatically.
4

Select metric or imperial units

Metric uses newtons, meters, newton-meters, and kilowatts. Imperial uses pounds, feet, pound-feet, and horsepower. Switch anytime — your inputs stay in place.
5

Read your result instantly

Both tabs update live as you type — no submit button needed.

What Each Value Means

Torque (N·m or lb-ft): A rotational (twisting) force equal to the applied force multiplied by the perpendicular distance from the pivot point to where the force acts. Measured in newton-meters (N·m) in metric or pound-feet (lb-ft) in imperial.
Power (kW or HP): The rate at which torque does work as something rotates, equal to torque multiplied by angular velocity (P = τ × ω). Measured in kilowatts (kW) in metric or horsepower (HP) in imperial.
Angular Velocity (rad/s): Rotational speed expressed in radians per second, calculated as RPM × 2π ÷ 60. This is the unit the underlying physics formula (P = τ × ω) actually uses — RPM is just a more intuitive everyday unit that gets converted behind the scenes.

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Frequently Asked Questions

What is the formula for torque?

Torque (τ) = Force × distance × sin(θ), where distance is the length of the lever arm from the pivot to where the force is applied, and θ is the angle between the force vector and the lever arm. When the force is applied perpendicular to the arm (θ = 90°), sin(90°) = 1, so the formula simplifies to the more familiar τ = F × r. This is the case most torque wrench and bolt-spec references assume by default.

How do you convert torque to horsepower?

Horsepower = Torque (lb-ft) × RPM ÷ 5252 in imperial units, or Power (kW) = Torque (N·m) × RPM ÷ 9549 in metric units. Both formulas come from the same physics relationship, P = τ × ω, where ω is angular velocity in radians per second (RPM × 2π ÷ 60). The constants 5252 and 9549 just fold the unit conversions into a single number so you don't have to convert RPM to rad/s by hand.

How do you convert horsepower to torque?

Rearrange the power formula: Torque (lb-ft) = Horsepower × 5252 ÷ RPM, or Torque (N·m) = Power (kW) × 9549 ÷ RPM. This is why low-RPM engines and motors need much more torque to produce the same horsepower as a high-RPM one — torque and RPM are inversely related for a fixed power output. Use the Torque/Power/RPM solver above and choose 'Torque' to solve this directly.

What's the difference between torque and power?

Torque is a rotational force — how hard something twists, measured in newton-meters or pound-feet. Power is the rate at which that twisting force does work over time, measured in watts, kilowatts, or horsepower. A diesel engine can produce huge torque at low RPM but modest peak power, while a high-revving gasoline engine can produce less torque but similar or greater power because power scales with RPM as well as torque (P = τ × ω).

Why does angle matter in the torque formula?

Torque depends on the component of force that is perpendicular to the lever arm, which is why the full formula includes sin(θ). Pulling straight along the length of a wrench handle (θ = 0°) produces zero torque no matter how hard you pull, because sin(0°) = 0 — all the force is wasted trying to stretch or compress the arm instead of rotating it. Pulling perpendicular to the handle (θ = 90°) transfers 100% of the force into rotation, which is why mechanics are taught to pull wrenches at a right angle whenever possible.