Torque Calculator
Calculate torque from force, distance, and angle – or solve the same relationship backward for any one unknown.
Inputs
The selected quantity becomes the calculated result; the other three are required inputs.
Nonnegative value; use a dot for decimals and commas only as thousands separators.
Magnitude of the applied force. A reverse calculation may require a value greater than zero.
Valid range: 0 – 180° or 0 – π radians. Torque magnitude uses the sine of this angle.
The turning moment about the pivot. This field is read-only when Torque is selected under Solve for.
Live results
Torque
60 N·m
0.5 m × 120 N × sin(90°) = 60 N·m
The force is perpendicular to the lever arm, so all 120 N contributes to rotation and the torque is at its maximum for this distance and force.
Calculation detail
| Quantity | Symbol | Current value | Role in the calculation |
|---|---|---|---|
| Distance from pivot | r | 0.5 m | Input lever-arm distance |
| Force | F | 120 N | Applied force magnitude |
| Angle | θ | 90° | Sets the perpendicular component |
| Moment arm | r sin(θ) | 0.5 m | Effective perpendicular distance |
| Perpendicular force | F sin(θ) | 120 N | Force component producing rotation |
| Torque | τ | 60 N·m | Calculated turning moment |
This table and the Excel workbook are generated from the same canonical SI model. Display units are converted only after the physics calculation is complete.
How to use this torque calculator
What this calculator does
This calculator applies the magnitude relationship τ = r × F × sin(θ) to a single force acting at a known distance from a pivot. It can calculate Torque, Force, Distance from pivot, or the principal Angle between r and F. It is useful for checking hand-tool leverage, door or hinge loading, shaft and lever problems, classroom mechanics exercises, and preliminary engineering estimates. It does not determine material strength, fastener safety, motor performance, bearing loads, or the net torque from several forces; those require a fuller free-body analysis and appropriate design factors. OpenStax provides a concise derivation and physical explanation in its section on torque in fixed-axis rotation.
When to use it
Use the calculator when you know any three quantities in the torque equation and need the fourth. Typical cases include estimating the turning effect of a wrench, determining the force needed at a handle, finding the lever length required for a target torque, or evaluating how a non-perpendicular pull reduces rotational effectiveness. The result is a scalar magnitude; clockwise or counterclockwise sign conventions are outside this calculator's scope.
How to calculate
- The calculator opens with a complete demonstration: 0.5 m, 120 N, and 90°, producing 60 N·m. The matching Excel workbook is immediately available.
- Choose the unknown in Solve for. That quantity becomes read-only, while the remaining three fields become required inputs.
- Replace the demonstration values using a dot as the decimal separator. Choose each unit from its adjacent selector; changing units converts the current value rather than merely relabeling it.
- Read the primary result, then use Moment arm, Perpendicular force, and Angle effectiveness to understand why the result changes.
- Select Download Excel to export the current validated inputs, outputs, equation detail, and assumptions as a real XLSX workbook. Reset clears all demonstration values and results; Excel export remains disabled until a complete valid state is entered again.
Input guide
Solve for is required and accepts Torque, Force, Distance, or Angle. It determines which field is calculated. Distance from pivot (r) is a nonnegative decimal distance measured from the rotation axis to the force application point; 0.5 m is a realistic example. Increasing distance increases torque in direct proportion when force and angle stay fixed. Do not substitute the object's total length unless the force is actually applied at its end. Distance unit accepts m, cm, mm, ft, or in and converts the current entry.
Force (F) is a nonnegative force magnitude, with 120 N as the startup example. Choose N, kN, or lbf under Force unit. More force produces proportionally more torque. A common mistake is entering mass in kilograms or pounds instead of force; weight must first be converted to force. Angle between r and F (θ) is required except when Angle is the selected unknown. Enter 0 – 180 in degrees or 0 – π in radians and choose the format under Angle unit. A 90° force is maximally effective, while 0° or 180° produces zero torque magnitude. The angle is between the lever-arm vector and force vector, not automatically the angle to the floor.
Torque (τ) is a nonnegative turning moment, with 60 N·m in the demonstration. It becomes an input when solving for Force, Distance, or Angle. Torque unit accepts N·m, kN·m, lbf·ft, or lbf·in. Do not enter energy in joules even though torque and energy share the same base dimensions; NIST distinguishes the SI unit name for moment of force as the newton meter rather than the joule.
Output guide and worked example
Primary result is the selected unknown in its chosen display unit. Moment arm is r × sin(θ), the effective perpendicular distance from the pivot to the force's line of action. Perpendicular force is F × sin(θ), the force component that creates rotation. Angle effectiveness is sin(θ) expressed as a percentage: 100% at 90°, 50% at 30° or 150°, and 0% at 0° or 180°. These are exact identities within the single-force model, while real-world measurements remain estimates subject to measurement uncertainty.
For the startup values, r = 0.5 m, F = 120 N, and θ = 90°. Since sin(90°) = 1, the moment arm is 0.5 m and the perpendicular force is 120 N. Therefore, τ = 0.5 × 120 × 1 = 60 N·m. If the same force were applied at 30°, sin(30°) = 0.5, so torque would fall to 30 N·m even though distance and force were unchanged.
Formula, assumptions, and reverse calculations
Torque depends on the portion of force perpendicular to the lever arm. That is why the sine term appears. A force directed along the lever arm may be large but creates no turning effect about the pivot. The Physics Classroom's torque lesson and vector-angle explanation illustrates how the lever arm, force, and angle work together.
Reverse calculations have additional domain limits. Solving for Force or Distance requires a nonzero effective lever arm, so the denominator cannot be zero. Solving for Angle requires τ ÷ (rF) to fall between 0 and 1. Because sin(θ) has the same value for supplementary angles, the calculator reports the principal angle from 0° to 90°; the supplementary solution 180° – θ creates the same torque magnitude.
Units, interpretation, and common mistakes
All calculations are performed internally in meters, newtons, radians, and newton meters. Display values are then converted to the selected units. The NIST conversion table for moment of force and torque units gives the authoritative relationship 1 lbf·ft = 1.355818 N·m. Keeping a single canonical unit system prevents mixed-unit errors and ensures that the page and workbook use the same numerical model.
The most common mistakes are measuring r from the wrong point, using mass instead of force, entering the complementary angle without understanding the geometry, and comparing torque values expressed in different units. High torque can result from high force, a long lever arm, a favorable angle, or a combination of all three. A low value does not necessarily mean the applied force is small; it may simply be nearly parallel to the lever arm. For safety-critical design, verify the actual load path, include all applied forces, and consult the relevant engineering standard or a qualified professional.