Worked examples
Wrench on a boltYou pull a 25 cm wrench with 150 N, perpendicular to the handle.
0.25 m x 150 N x sin(90 deg) = 37.5
37.5 N.m = 27.6586 ft.lb
Maximum torque: the force is at 90 degrees, so sin(theta) = 1.
How hard must you push for 110 N.m?Wheel lug-nut spec is 110 N.m. Your wrench is 0.30 m long; you push at 90 degrees.
F = 110 / (0.30 x sin 90 deg) = 366.6667
366.6667 N = 82.4299 lbf
That is why a longer breaker bar makes the job easier: double the arm, halve the force.
Two angles, one torqueYou need 25 N.m from a 0.5 m arm pushed with 100 N. At what angle?
sin(theta) = 25 / (0.5 x 100) = 0.5 = 0.5
theta = 30 deg or 150 deg
Both angles give the same perpendicular component; pick the one that fits your setup.
Converting 50 N.mYour manual lists 50 N.m; your wrench reads imperial.
50 / 1.3558179483314004 and 50 / 0.1129848290276167 = 36.8781
36.8781 ft.lb = 442.5373 in.lb
Matches the converter panel exactly.
Frequently asked questions
What is the torque formula?
Torque is tau = r x F x sin(theta). Here r is the lever arm (distance from the pivot to where the force is applied), F is the force, and theta is the angle between the lever-arm direction and the force direction. The result is in newton meters when r is in meters and F is in newtons.
How do I calculate torque from force and distance?
Multiply the lever arm by the force and by the sine of the angle. Example: a 0.5 m wrench pulled with 100 N at 90 degrees gives 0.5 x 100 x sin(90 deg) = 50 N.m, which is 36.8781 ft.lb. Enter the three values in the solver above and it does this live, in any units.
Why does the angle between the force and the wrench matter?
Only the perpendicular component of the force turns the bolt, and that component is F x sin(theta). At 90 degrees sin(theta) = 1, so you get maximum torque. At 0 or 180 degrees the force points along the wrench and produces zero torque: pushing straight along the handle does nothing.
Can torque be negative?
The sign only records rotation direction, not a different physical size. By convention this calculator treats counter-clockwise as positive and clockwise as negative. A torque of -50 ft.lb has the same magnitude as +50 ft.lb; it just turns the other way.
How do I solve for the force instead of the torque?
Rearrange the formula: F = tau / (r x sin(theta)). Example: to reach a 110 N.m lug-nut spec with a 0.30 m wrench at 90 degrees, you need F = 110 / 0.30 = 366.6667 N, about 82.4299 lbf. Choose Solve for Force F in the solver to get this instantly.
Why does the angle solver return two answers?
Because sin(theta) = sin(180 deg - theta). If sin(theta) = 0.5, both 30 degrees and 150 degrees satisfy the equation. Example: tau = 25 N.m with r = 0.5 m and F = 100 N gives theta = 30 deg or 150 deg. Both are physically valid; pick the one matching your setup.
When does the angle solver say there is no solution?
When the requested torque exceeds r x F, so tau/(r x F) is greater than 1 and no angle can produce it. Example: asking 60 N.m from a 0.5 m arm and 100 N force is impossible because the maximum at 90 degrees is only 50 N.m. Increase the arm or the force.
Is torque the same as work or energy?
Numerically, 1 N.m of torque equals 1 joule, because both multiply force by distance. Physically they differ: torque is a rotational vector (it has a direction of twist), while work and energy are scalars. For work and energy calculations use our dedicated work calculator.
What is the difference between this calculator and a bolt torque calculator?
This page solves the general physics formula tau = r x F x sin(theta). A bolt torque calculator answers a different question: what tightening torque a fastener needs, from T = K x F x d (friction factor times clamp force times diameter). For tightening bolts, use our bolt-torque tool.
What is the difference between this calculator and motor torque?
Motor torque is derived from power and speed: T = HP x 5252 / RPM. This page never uses horsepower or RPM; it works from lever arm, force and angle. For electric motors and engines, use our electric-motor-torque tool.
What torque units does this calculator support?
Six: N.m, kN.m, ft.lb, in.lb, kgf.m and oz.in. The exact bridges are 1 ft.lb = 1.3558179483314004 N.m, 1 in.lb = 0.1129848290276167 N.m, 1 kgf.m = 9.80665 N.m, and 1 oz.in = 0.007061551814226 N.m. The converter panel translates any value between all six.
How precise should my torque result be?
A typical click-type torque wrench is accurate to about plus or minus 3 to 4 percent, so 3 or 4 significant figures are plenty in the workshop; this tool offers up to 8 decimals for engineering checks. Always follow the equipment manual over any table or calculator.