Torque Calculator
Torque from force and radius, force from torque, or power from torque and RPM — in N·m, lb·ft, watts and horsepower, with the 5252 constant explained.
Torque Calculator: with the default inputs, solved value is 50.
Perpendicular to the arm. 1 lbf = 4.448 N; a 10 kg mass in Earth gravity pulls 98.1 N.
Distance from the axis to where the force acts.
Used when solving for force or power. 1 lb·ft = 1.3558 N·m.
Revolutions per minute. Also used to report the power any solved torque would deliver.
N·m, newtons or watts, depending on what you are solving for.
- In words
- 100 N at 0.5 m is 50 N·m (36.878 lb·ft)
- Torque (N·m)
- 50
- Torque (lb·ft)
- 36.8781
- Force (N)
- 100
- Force (lbf)
- 22.4809
- Angular velocity (rad/s)
- 314.1593
- Power
- 15,707.96 W
- Power (hp)
- 21.065
Assumptions
- Force acts perpendicular to the lever arm; any component along the arm contributes nothing.
- Steady rotation — torque needed to accelerate a rotating mass (τ = Iα) is not included.
- No friction or drivetrain losses.
- Rigid bodies, and a single point of force application.
| RPM | Power (W) | Power (kW) | Power (hp) |
|---|---|---|---|
| 500 | 2,618 | 2.62 | 3.51 |
| 1,000 | 5,236 | 5.24 | 7.02 |
| 1,500 | 7,854 | 7.85 | 10.53 |
| 2,000 | 10,472 | 10.47 | 14.04 |
| 3,000 | 15,708 | 15.71 | 21.06 |
| 4,000 | 20,944 | 20.94 | 28.09 |
| 5,252 | 27,499.4 | 27.5 | 36.88 |
| 6,000 | 31,415.9 | 31.42 | 42.13 |
At constant torque, power rises in a straight line with speed. The 5,252 RPM row is where the horsepower and pound-feet numbers are numerically equal — every engine dyno chart crosses there, and it is an artefact of the unit conversion, not a property of the engine.
How this is worked out
The formula
Torque τ = F × r (force perpendicular to the arm) Force F = τ ÷ r Angular vel. ω = 2π × RPM ÷ 60 (radians per second) Power P = τ × ω = τ × RPM ÷ 9.5493 (N·m, RPM → watts) Imperial hp = lb·ft × RPM ÷ 5252 1 lb·ft = 1.35582 N·m, 1 lbf = 4.44822 N, 1 hp = 745.7 W
Open How it’s calculated above to see this worked through with your own numbers.
What you enter
- Solve for
- Choose one of 3 options.Torque — from force and radius · Force — from torque and radius · Power — from torque and RPM
- Force at the end of the arm
- Perpendicular to the arm. 1 lbf = 4.448 N; a 10 kg mass in Earth gravity pulls 98.1 N.defaults to 100
- Radius / lever arm
- Distance from the axis to where the force acts.in mm, cm, m, in, ft · 0 or more · defaults to 0.5
- Torque
- Used when solving for force or power. 1 lb·ft = 1.3558 N·m.defaults to 50
- Rotational speed
- Revolutions per minute. Also used to report the power any solved torque would deliver.0 or more · defaults to 3000
What you get back
- Solved valuemain answer
- N·m, newtons or watts, depending on what you are solving for.
- In words
- Torque (N·m)
- Torque (lb·ft)
- Force (N)
- Force (lbf)
- Angular velocity (rad/s)
- Power
- Power (hp)
What this assumes
- Force acts perpendicular to the lever arm; any component along the arm contributes nothing.
- Steady rotation — torque needed to accelerate a rotating mass (τ = Iα) is not included.
- No friction or drivetrain losses.
- Rigid bodies, and a single point of force application.
About this calculator
Torque is the rotational equivalent of force: how hard something twists. It is the force applied multiplied by the distance from the axis it acts at, which is why a long breaker bar loosens a bolt a short spanner will not — same hand, more lever arm, more torque.
The three things this solves
Torque from force and radius is the definition, τ = F × r. Note the perpendicular part: only the component of force at right angles to the arm does anything. Pulling along the spanner handle produces zero torque no matter how hard you pull, and pulling at 45° gives you 71% of the torque you think you are applying.
Force from torque runs it backwards — the question a torque wrench answers. A bolt spec of 50 N·m and a 300 mm wrench means 167 N at the end of the handle, about 17 kg hanging off it. Hold the wrench halfway along and you need twice the force for the same result.
Power from torque and RPM is the one with the constant in it. Power is the rate of doing work, and for rotation that is torque times angular velocity: P = τω. RPM is not angular velocity — you have to convert, ω = 2π · RPM / 60 — and that 2π/60 is where all the magic constants come from. In SI, P(W) = τ(N·m) × RPM / 9.5493. In imperial, hp = lb·ft × RPM / 5252, and the 5252 is just 33,000/2π, dragged in from James Watt's definition of a horsepower as 33,000 ft·lbf per minute.
That constant is also why every dyno graph shows the horsepower and torque curves crossing at exactly 5,252 RPM. It is not telling you anything about the engine — it is the point where the unit conversion factor equals one.
Torque versus power, in practice
Torque is what breaks the bolt; power is what determines how fast you can do it repeatedly. An engine making 400 N·m at 2,000 RPM and one making 200 N·m at 4,000 RPM produce identical power, and a gearbox can turn either into the other — that is exactly what gearing is for. Peak torque tells you where an engine pulls hardest; peak power tells you the best it can do with the right gear.
Where this model breaks down
- It assumes a static or steady situation. Accelerating a rotating mass needs extra torque, τ = Iα, where I is the moment of inertia — that is not modelled here.
- Friction and preload. On a threaded fastener, most of your torque is fighting friction under the head and in the threads, not stretching the bolt. The torque-to-clamp-load relationship shifts hugely with lubrication, which is why oiled and dry torque specs differ by 20–30% and why critical joints are tightened by angle or bolt stretch instead.
- Efficiency. Power out of a gearbox or belt is less than power in. Nothing here subtracts losses.
- Units. N·m and joules have identical dimensions but are not interchangeable: a joule is energy, a newton-metre of torque is a moment. Never add them.
Frequently asked questions
▸What is the torque formula?
τ = F × r: the force applied times the perpendicular distance from the axis of rotation. Doubling the lever arm doubles the torque for the same force.
▸How do I convert torque to horsepower?
hp = torque in lb·ft × RPM ÷ 5252, or in SI, watts = N·m × RPM ÷ 9.5493. Both come from P = τω with ω in radians per second.
▸Why is 5252 the magic number?
It is 33,000 ÷ 2π. One horsepower was defined as 33,000 foot-pounds per minute, and converting revolutions to radians brings in the 2π. It is a unit artefact, which is why torque and power curves always cross there.
▸Is a newton-metre the same as a joule?
Dimensionally yes, physically no. A joule is energy — force along a distance. A newton-metre of torque is a force at right angles to a distance. Keep them in separate columns.
▸Does more torque mean more power?
Only at the same RPM. Power is torque times speed, so a low-revving engine with huge torque and a high-revving one with modest torque can make identical power. Gearing converts between the two.
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