Example 1
F = 20 N, r = 0.3 m, α = 90° → M = 6.
Torque calculator
Type F [N], r [m] and angle α. The calculator computes M = F r sinα: 20 N, 0.3 m and 90° is 6 N·m, and at 30° you get 3 N·m. N·m of torque is not a joule of work.
Lever: F₁r₁ = F₂r₂. Point I: I = m·r². Energy: Eₖ = ½Iω².
Result
Force F, Arm r and Angle α (degrees). The result shows up here.
How it works
Torque is M = F r sinα. At 20 N, 0.3 m and 90°: sin 90° = 1, so M = 6 N·m. The same F and r at 30° give 3 N·m, because sin 30° = 1/2. At 0° or 180° torque is zero: the force runs along the arm and does not twist. 10 N on 0.6 m at 90° is 6 N·m again.
The form has three fields: F in newtons, r in meters, α in degrees. The result is in N·m. That is not a joule of work, even though the dimensions match. Torque is twist. r must be positive. A comma and a period are the same r: 0,3 and 0.3.
Typed 0° gives M = 0. Typed 0 in F also gives M = 0. All three fields need a number before 6 N·m can appear. Measure α from the arm to the force, not from the floor, unless the problem says otherwise.
Two arms live on lever equilibrium: F₁ r₁ = F₂ r₂. Here one torque. Point I and rotational Eₖ take other inputs.
F⊥ = F sinα is the perpendicular component. The calculator multiplies it by r. A 0.3 m wrench at 20 N and 90° is the 6 N·m example.
Type 20, 0.3 and 90, click Calculate, and match 6 N·m. Then change the angle to 30 and see 3 N·m. The header symbol does not tighten a bolt.
How to use
- In the first field enter F in newtons, for example 20.
- In the second enter r in meters, for example 0.3. In the third, α in degrees, for example 90.
- Click Calculate. The calculator computes F r sinα. 20, 0.3 and 90 give 6 N·m. At 30° that is 3 N·m.
- Typed 0° gives M = 0. r must be positive. All three fields need a number.
- For two arms, open lever equilibrium. Here it stays one torque.
Formula
M = F·r·sinα
F⊥ = F sinα
Unit: N·m.
M, F, r, and α for torque
One torque: M = F·r·sinα. 20 N, 0.3 m and 90° is 6 N·m. At 30° you get 3 N·m. N·m here is not a joule.
- M
- Torque [N·m]. 20 × 0.3 × 1 = 6. At 0° it is zero: force along the arm.
- F
- Force [N], 20 N in the example. The perpendicular part is F sinα.
- r
- Arm from the axis to the point of application [m]. 0.3 m. Must be positive.
- α
- Angle in degrees between F and the arm. 90° gives sin = 1. 30° gives 1/2.
Real-life examples
Example 2
Same F and r, α = 30° → half M.
Example 3
F = 10 N, r = 0.6 m, α = 90°.
Example 4
F = 5 N at handle r = 0.8 m, α = 90°.
Example 5
F = 150 N, r = 0.15 m, α = 90°.
Example 6
F = 40 N, r = 0.4 m, α = 10°.
Example 7
Force along the arm: M = 0.
Example 8
F = 50 N, r = 0.25 m, α = 90°.
Example 9
F = 30 N, r = 0.2 m, α = 60°.
Ways to use this calculator
- You compute 6 N·m from 20 N on a 0.3 m arm at 90°.
- You compare 90° with 30° at the same F and r.
Frequently asked questions
How much M at 20 N, 0.3 m and 90°?
Torque is 6 N·m. Sin 90° is one, so you compute 20 × 0.3. At 30° you get half, 3 N·m.
Which units do I type?
Force F [N], radius r [m], angle α in degrees. Result M [N·m]. That is not a joule, even though 1 N·m = 1 J in work.
What torque at 0° or 180°?
Torque is 0 N·m. The force runs along the arm and does not twist. Sin 0° and sin 180° are zero.
Where is the two-arm balance?
On the lever-balance page. There two torques cancel. Here you compute one M = F r sinα.
Is N·m a joule?
In work, yes, 1 N·m = 1 J. For torque you keep N·m, so twisting is not confused with energy.
Does a comma in 0.3 work?
Yes. 0.3 and 0,3 are the same r [m]. A comma and a period mean the same value.
Is r the wrench length?
It is the distance from the axis to the point where F is applied. On a wrench that is often the handle length, but only if you measure to the nut axis.
How much at 10 N, 0.6 m and 90°?
Torque is 6 N·m. Same product as 20 N on 0.3 m: half the force, twice the arm.
What does F⊥ mean?
The force component perpendicular to the arm, F sinα. At 90° F⊥ = F. At 30° F⊥ is half of F.
Do I measure α from the floor?
No. α is the angle between vector F and the arm, not the angle to the floor. 90° means the force is perpendicular to r.
Knowledge sources
The formula is the school one. Units follow SI; NIST SP 330 and BIPM define the measures, not your result.
Page updated in 2026.