80 N at 0.25 m, perpendicular
τ = r × F × sin(θ)
0.25 × 80 × 1 = 20 N·m. Changing the angle to 30° gives 10 N·m.
Force about a pivot
Torque Calculator
Find torque magnitude, applied force, or distance from a pivot. Account for the force angle and convert metric or US customary units.
Calculate torque, force, or distance
Torque magnitude
Enter the known values and angle, then select Calculate.
- Torque in N·m
- Force in newtons
- Distance from pivot in meters
- Angle
- Perpendicular moment arm, r sin(θ)
- Perpendicular force, F sin(θ)
- Formula
Calculation steps
≈ marks rounding or numerical trigonometry. Calculations run in your browser. Press Enter to calculate. Successful results appear in this tab's Recent calculations.
Three worked examples
12 N·m at 0.4 m and 30°
F = τ ÷ [r × sin(θ)]
12 ÷ (0.4 × 0.5) = 60 N. The perpendicular moment arm is 0.2 m.
18 lbf·ft from 12 lbf at 90°
r = τ ÷ [F × sin(θ)]
18 ÷ (12 × 1) = 1.5 ft, or 18 in. This is the pivot-to-application distance.
Model, units, and rounding
This calculator uses the magnitude of torque from one applied force about a pivot: τ = rF sin(θ). It does not combine multiple forces, assign rotation direction, or calculate angular acceleration. Reference: OpenStax — Torque.
Conversions use exact definitions: 1 kN = 1,000 N, 1 ft = 0.3048 m, 1 in = 0.0254 m, and 1 lbf = 4.4482216152605 N. Therefore 1 lbf·ft = 1.3558179483314004 N·m and 1 lbf·in = 0.1129848290276167 N·m. References: NIST conversion factors and NIST exact pound-force definition, note 23.
Torque and force inputs must be nonnegative. A supplied distance must be positive. At 0° or 180°, torque is zero and cannot determine a unique force or distance; a nonzero torque is inconsistent. Zero force likewise cannot determine distance. With a positive divisor, zero torque gives a zero force or a zero inferred distance. A zero inferred distance places the force at the pivot.
Inputs accept at most 64 characters, 15 integer digits, and 10 decimal places. Numeric fields do not accept units, expressions, or scientific notation. Hidden inputs are disabled and ignored. Angle inputs use degrees from 0 through 180; radians are not accepted.
Unit conversions and arithmetic use exact fractions. Sines of 0°, 30°, 90°, 150°, and 180° are exact here; other angles use a private 120-significant-digit numerical calculation. Only final displays are rounded. Halfway values round up, trailing zeros are omitted, and ≈ marks rounding or numerical trigonometry. Tiny nonzero values that round to zero receive a notice. Changing precision or result units does not add a recent-calculation entry.
Common questions
Is torque in N·m the same as energy in joules?
No. Torque and energy share dimensions but describe different quantities. This tool labels torque N·m, not J. See NIST SI derived units.
Why do 30° and 150° give the same magnitude?
Their sines are both 0.5. Both produce half the perpendicular-force torque for the same force and distance. Magnitude alone does not specify rotation direction.
Can this choose a bolt tightening torque?
No. Enter a known force, distance, and angle to evaluate this model. The calculator does not select fastener specifications, determine clamp load, or account for thread friction.
Why is a tiny nonzero angle different from zero?
An angle such as 0.0000000001° still has a nonzero sine. Inverse calculations can therefore produce a very large finite answer. Exactly 0° or 180° makes that inverse undefined, so the tool explains the ambiguity or inconsistency instead of dividing by zero.