Enter the force, lever arm length and angle to get the torque — in newton-metres, the unit of rotational force.
What Is a Torque Calculator?
A torque calculator applies τ = F × r × sin(θ): 50 N × 0.3 m × sin(90°) = 15.00 N·m. Torque is rotational force — what tightens bolts and what motors produce. Maximum torque comes at 90° (pushing perpendicular); pushing along the lever (0°) gives zero. Car engines quote it in N·m (or lb-ft in the US).
How to Use
- Enter the force in newtons.
- Enter the lever length in metres.
- Enter the angle in degrees.
- Click “Calculate Torque”.
Formula
τ = F × r × sin(θ).
Worked Example
50 N × 0.3 m × sin(90°) = 15.00 N·m.
How It Works, In Plain Words
Torque is a turning effect, and the formula τ = F × r × sin(θ) has three ingredients. F is the force, in newtons — how hard you push or pull. r is the lever length, in metres — the distance from the pivot (the bolt, the axle, the hinge) to the point where the force is applied. θ (theta) is the angle between the lever and the direction of the force. Multiply force by lever length, then scale by sin(θ): in the worked example, 50 N × 0.3 m × sin(90°). Because sin(90°) is exactly 1, the example reduces to 50 × 0.3 = 15.00 N·m.
The sine term is the part people forget. Only the component of force acting at right angles to the lever actually turns it. Push along the lever, at 0°, and sin(0°) is 0 — no torque at all, however hard you push. Push at 90° and every newton counts in full. Between the two, the tool works out the effective share for you, which is why the angle field exists alongside force and length.
Real-World Uses
A home mechanic changing a wheel uses the calculator to sanity-check a torque figure from the car’s manual: the manual states the tightness in N·m, and the tool shows what that means in terms of hand force on the wrench they own — the 50 N on a 0.3 m lever giving 15.00 N·m is exactly that kind of check. A physics student uses it for homework on rotational motion, verifying hand calculations of τ = F × r × sin(θ) before submitting them. And a buyer comparing two motors or an engine for a project uses it to put quoted figures on a common footing, remembering that a torque figure only tells the whole story alongside the RPM at which it is produced.
Benefits
- The angle handled properly (sin θ)
- Result in N·m
- Useful for mechanics and motor specs
- Simple three-input tool
Features of Our Tool
- Instant results in your browser
- No sign-up, no download, 100% free
- Works on mobile, tablet and desktop
- Clear step-by-step explanation below the tool
- Private — your entries never leave your device
Common Mistakes
- Forgetting the angle — only the perpendicular component counts
- Mixing N·m with lb-ft (1 N·m = 0.7376 lb-ft)
- Using weight (kg) instead of force (N)
Common Mistakes to Avoid
The most damaging slip is entering the lever length in centimetres. This tool expects metres, so a 0.3 m wrench entered as 30 inflates the answer a hundredfold — if your result looks absurdly large, check the units first. Next, using body weight or a mass in kilograms as the “force”: the field needs newtons, and kilograms measure mass, not force. Angle errors follow: the angle is between the lever and the force direction, and entering the complement quietly changes the sine and the result. Finally, unit mix-ups when comparing results — a figure in N·m is not a figure in lb-ft, and at 1 N·m = 0.7376 lb-ft the two differ enough to under- or over-tighten a fastener.
FAQ
What is 50 N at 0.3 m and 90°?
15.00 N·m.
What is torque?
Rotational force — force times lever arm times sin(angle).
Why does angle matter?
Only the perpendicular component of force creates torque — maximum at 90°.
What is N·m vs lb-ft?
1 N·m = 0.7376 lb-ft — metric vs imperial torque units.
How is motor torque quoted?
In N·m (or lb-ft) — often with the RPM it occurs at.
Is torque the same as force?
No. Force is a straight-line push or pull measured in newtons; torque is the turning effect of a force around a pivot, measured in newton-metres. Torque depends on the force, the lever length and the angle together — the same force gives a strong turning effect at the end of a long lever and almost none applied close to the pivot.
Why does a longer wrench make tight bolts easier?
Because at 90° the torque is simply force multiplied by lever length. A longer wrench lets the same hand force act through a longer lever, so it delivers more torque to the bolt. Nothing is free — your hand travels further — but the turning effect at the fastener is what loosens it.