Calculate torque, force, lever arm, or angle. Enter any three known values in |τ| = rF sin(θ) and get the answer, conversions, diagram, and complete worked steps. Use newton-metre (newton-meter), pound-force foot (lbf·ft, lb-ft, or ft-lb), and other common units.
Inputs
Advanced: multiple forces and net torque
Each row uses τ = rF sin(θ). Counterclockwise is positive; clockwise is negative.
Add forces to calculate signed and net torque.
Results
Torque
15 N·m
Calculated from the full torque relation.
Supporting values
Calculation steps
Torque in all supported units
Torque unit
Value
Educational use only. This page handles idealized statics and unit conversion. It does not evaluate bolt preload, thread friction, wrench calibration, fatigue, material limits, or design-code compliance.
How torque is calculated
Torque, or moment of force, is the turning effect of a force about a pivot. This calculator uses the magnitude relation |τ| = rF sin(θ), where r is the physical distance from pivot to application point, F is force, and θ is the angle between their vectors. The perpendicular moment arm is r⊥ = r sin(θ), so |τ| = Fr⊥.
How to use this calculator
Choose torque, force, lever arm, or angle as the unknown.
Enter the known values and select their units.
Use the angle between the lever-arm vector and force direction, not an angle measured from a perpendicular line.
Select Calculate, then review the answer, unit conversions, diagram, and worked steps.
Formulas
|τ| = rF sin(θ)
F = |τ| / (r sin(θ))
r = |τ| / (F sin(θ))
θ = sin−1(|τ|/(rF)); a supplementary solution may also apply.
Torque reference tables
Angle versus torque factor
Angle
sin(θ)
Maximum torque
0° / 180°
0
0%
15° / 165°
0.2588
25.88%
30° / 150°
0.5
50%
45° / 135°
0.7071
70.71%
60° / 120°
0.8660
86.60%
90°
1
100%
Variables and units
Symbol
Meaning
Typical units
τ
Torque magnitude
N·m, lbf·ft
F
Force magnitude
N, kN, lbf
r
Pivot-to-force distance
m, cm, ft, in
θ
Angle between r and F
degrees, radians
r⊥
Perpendicular moment arm
m, ft, in
Common torque conversions
Starting value
Equivalent
1 N·m
0.737562 lbf·ft
1 N·m
8.85075 lbf·in
1 lbf·ft
1.355818 N·m
1 lbf·in
0.112985 N·m
1 kgf·cm
0.0980665 N·m
1 kgf·m
9.80665 N·m
Common mistakes
Radius, not diameter: divide diameter by two.
Physical length versus moment arm: r⊥ = r sin(θ).
Wrong angle reference: measure between r and F.
Mixed units: convert force and length to a consistent system.
Torque versus energy: both share N·m dimensions, but energy is written J.
Torque versus power: power also requires angular speed, P = τω.
Fully worked torque examples
1. Calculate torque — SI wrench
Given F = 50 N, r = 30 cm, and θ = 90°. Convert r: 30 cm × 0.01 m/cm = 0.30 m.
Interpretation: the perpendicular push applies 15 N·m about the bolt.
2. Calculate required force — US customary breaker bar
Target τ = 85 lbf·ft, r = 18 in, and θ = 90°. Convert: 85 × 1.355817948 = 115.2445 N·m; 18 × 0.0254 = 0.4572 m.
F = 115.2445 / [(0.4572)sin(90°)] = 252.066 N. Convert: 252.066 / 4.448221615 = 56.67 lbf.
Interpretation: about 56.7 pounds-force at the end of the 18-inch bar reaches the target ideally.
3. Calculate required lever length — SI hand lever
Given τ = 60 N·cm, F = 12 N, and θ = 90°. Convert torque: 60 × 0.01 = 0.60 N·m.
r = 0.60 / [(12)sin(90°)] = 0.050 m. Convert: 0.050 × 100 = 5.0 cm.
Interpretation: apply the 12 N perpendicular force at least 5 cm from the pivot.
4. Calculate angle — US customary pedal
Given τ = 30 lbf·ft, F = 80 lbf, and r = 12 in. Convert r: 12 in ÷ 12 = 1 ft; the consistent ratio is 30 / [(1)(80)] = 0.375.
θ = sin−1(0.375) = 22.02°; the supplementary solution is 180° − 22.02° = 157.98°.
Interpretation: either direction has the same torque magnitude; the actual geometry determines which angle applies.
Methodology and sources
Author: Starlight RoboticsUpdated: 15 July 2026Review status: equation and constants checked against the sources below; no individual credentialed reviewer is claimed.
Calculation method: inputs are converted to N, m, N·m, and radians; the selected rearrangement of |τ| = rF sin(θ) is evaluated at full JavaScript precision; only the displayed answer is rounded. The angle solver rejects |τ|/(rF) > 1 as physically impossible for this model.
How do I calculate the angle in the torque equation?
Rearrange the magnitude equation to theta = arcsin(|tau|/(rF)). The ratio must be between 0 and 1. Between 0 and 180 degrees, most nonzero ratios have a principal angle and a supplementary angle that produce the same torque magnitude.
Why are torque and energy both expressed with N·m?
They share the same base dimensions but describe different quantities. Torque is a vector-like moment of force and is written N·m; energy is a scalar and the special SI name joule, J, is used.
Should I enter radius or diameter for the lever arm?
Enter the radius: the distance from the pivot axis to the force application point. If only a diameter is given, divide it by two before entering it.
How are clockwise and counterclockwise torque signed?
A common planar convention treats counterclockwise torque as positive and clockwise torque as negative. The single-force solver reports magnitude; Advanced net torque applies that sign convention.
Are lb-ft and ft-lb the same torque unit?
In torque specifications, lb-ft and ft-lb are commonly used aliases for pound-force foot, properly written lbf·ft. This calculator labels pound-force explicitly so it is not confused with pound-mass.
Why can’t torque be converted directly to horsepower?
Torque is not power. Rotational power also requires angular speed: P = tau omega. You need rpm or another rotational-speed value before converting the resulting power to horsepower.
What is the difference between arm length and perpendicular moment arm?
Arm length r runs from the pivot to the force application point. The perpendicular moment arm r_perp is the shortest distance from the pivot to the force line of action and equals r sin(theta).
