Torque Calculator
Calculate torque, force, lever arm, angle, power, RPM, moment of inertia, or angular acceleration with automatic unit conversion.
Calculator is for informational purposes only. Terms and Conditions
For a force acting at a distance from a pivot, θ is the angle between the lever arm and force vector.
Choose the torque relationship
Choose the relationship that matches the values you know, then select the unknown.
Enter the known values
Mix metric and U.S. customary units as needed; changing a unit preserves the same physical quantity.
For force-angle torque, use the included angle between the lever arm and the force direction. A 90° force is perpendicular and produces maximum torque.
Result
Primary answer first, followed by equivalent units, useful checks, warnings, and transparent solution steps.
Result details
- Check—
Show calculation stepsReview conversions, equations, substitutions, assumptions, and reverse checks
- Enter valid values to see the complete calculation.
Torque Visual
The diagram shows the lever arm, applied force, force angle, and rotation direction for the force × lever arm method.
Method, Sources, and Assumptions
Calculation basis, authoritative references, unit conversions, limitations, and final verification requirements.
The calculator uses standard rotational mechanics relationships and performs all calculations in canonical SI units before converting the displayed answer.
- The force × lever-arm mode treats the entered force as an idealized force applied at a known point and angle.
- The power mode assumes the entered power is mechanical power at the same shaft where torque and speed are evaluated.
- The rotational-dynamics mode uses net torque about a fixed axis; moment of inertia must be referenced to that same axis.
- This calculator is not a bolt-tightening specification, preload model, shaft-rating check, gearbox-rating check, or code-compliance tool.
Torque Calculator Guide
The Torque Calculator above solves three closely related rotational-mechanics problems: torque from force, lever arm, and angle; torque, power, or speed from rotating-shaft data; and net torque, moment of inertia, or angular acceleration from rotational dynamics. For the most common calculation, enter force, lever arm distance, and the included force angle to find torque using \(\tau=rF\sin\theta\). The tool can also solve that relationship in reverse for force, distance, or angle. Use the result as an engineering or physics calculation, not as a bolt-tightening specification or an automatic equipment rating.
- Primary use
- Force, lever-arm, and angle torque calculations
- Other modes
- Power and RPM; rotational dynamics
- Key geometry
- The angle is measured between the lever arm and force vector
Fast mental check
When force is perpendicular to the lever arm, \(\theta=90^\circ\) and \(\sin\theta=1\), so torque is simply force times distance. A 100 N force applied 0.30 m from the pivot therefore produces 30 N·m. At any other angle between 0° and 180°, the torque magnitude cannot exceed that 30 N·m maximum for the same force and distance.
How to Use the Torque Calculator
Start by choosing the calculation method that matches the values you actually know. The calculator changes the available unknowns, visible inputs, equation, result units, and validation rules with that selection.
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Choose the calculation method
Force × Lever Arm is for a force acting about a pivot or axis. Power, Torque & RPM is for a rotating shaft at one operating point. Rotational Dynamics relates net torque, mass moment of inertia, and angular acceleration.
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Choose what to solve for
Force × Lever Arm can solve for torque, force, lever arm, or angle. Power mode can solve for torque, mechanical power, or rotational speed. Rotational Dynamics can solve for net torque, moment of inertia, or angular acceleration.
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Enter only the known quantities
Use the unit selector next to each value. The calculator converts values internally before solving, so SI and U.S. customary units can be mixed without manually converting each input first.
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Check the result details and calculation steps
Review equivalent units, reverse checks, angle information, or other mode-specific details. The force-and-lever-arm diagram is especially useful for confirming that the angle was interpreted from the lever arm to the force direction.
Angle entry is the most common geometry error
Enter the included angle between the lever arm and the applied force. A perpendicular push or pull is 90°, not 0°. A force directed along the lever arm at 0° or 180° passes through the pivot line and produces zero torque about that pivot.
Torque Calculation Methods
The calculator uses exact closed-form mechanics relationships. The correct equation depends on whether torque comes from an applied force, a rotating shaft transmitting power, or a rigid body undergoing angular acceleration.
Force, lever arm, and angle
In plain language: multiply the distance from the pivot by the force and by the sine of the angle between them. OpenStax gives the same fixed-axis torque magnitude relationship and identifies \(r\sin\theta\) as the perpendicular moment arm.
Reference: OpenStax University Physics, Section 10.6: Torque.
Power, torque, and rotational speed
Here \(n\) is rotational speed in revolutions per minute and \(\omega\) is angular speed in radians per second. Solving for torque gives \(\tau=P/\omega\). The power and speed values must describe the same shaft and operating point.
Net torque and angular acceleration
Net torque equals mass moment of inertia about the chosen axis multiplied by angular acceleration about that same axis. OpenStax presents this as Newton’s second law for fixed-axis rotation.
Reference: OpenStax University Physics, Chapter 10 Key Equations.
Variables used by the calculator
- \(\tau\)
- Torque Rotational moment about a chosen pivot or axis.
- \(r\)
- Lever arm distance Distance from the pivot or axis to the point where the force is applied.
- \(F\)
- Applied force Magnitude of the push or pull acting at the specified point.
- \(\theta\)
- Force angle Included angle between the lever arm and force vector.
- \(P\)
- Mechanical power Rate of mechanical work transmitted by the rotating shaft at the entered operating point.
- \(\omega\)
- Angular speed Rotational speed expressed in radians per second.
- \(I\)
- Mass moment of inertia Resistance of the mass distribution to angular acceleration about a specified axis.
- \(\alpha\)
- Angular acceleration Rate of change of angular velocity using the selected positive/negative rotational convention.
Why two angles can solve the same torque magnitude
When solving \(\tau=rF\sin\theta\) for an angle between 0° and 180°, \(\sin\theta=\sin(180^\circ-\theta)\). Unless the solution is exactly 90°, a positive torque magnitude can therefore correspond to a principal angle and a supplementary angle. The calculator reports this ambiguity instead of silently returning only one physical angle.
Worked Torque Example
Use the calculator’s default force-and-lever-arm example as a quick independent check: a 100 N force acts 0.30 m from a pivot at 90°.
Substitute into the torque equation
Because \(\sin 90^\circ=1\), the entire 100 N force acts perpendicular to the 0.30 m lever arm.
Result
Torque = 30 N·m
Using the NIST conversion factor \(1\,\text{lbf}\cdot\text{ft}=1.355818\,\text{N}\cdot\text{m}\), the same torque is about 22.13 lbf·ft.
Independent verification
The perpendicular moment arm is \(r_\perp=r\sin\theta=(0.30)(1)=0.30\) m. The alternative form \(\tau=Fr_\perp\) gives \((100)(0.30)=30\) N·m, reproducing the result by a second route. If the angle were changed to 30° while force and distance stayed fixed, torque would fall to 15 N·m because \(\sin 30^\circ=0.5\).
How to Interpret Torque Results
A torque number is meaningful only with its axis, sign convention, operating point, and application. The checks below help distinguish a correct calculation from a result that is mathematically valid but misapplied.
Force mode
For fixed force and lever-arm distance, torque scales with \(\sin\theta\). At 90° the magnitude is maximum; at 30° it is 50% of that maximum; at 0° or 180° it is zero.
Power mode
For fixed mechanical power, torque is inversely proportional to angular speed. Halving RPM while holding shaft power constant doubles the calculated torque.
Dynamics mode
For fixed moment of inertia, net torque changes linearly with angular acceleration. Doubling \(\alpha\) requires twice the net torque.
Physical bounds and sanity checks
- For force mode, the torque magnitude must satisfy \(|\tau|\le rF\). A requested magnitude greater than \(rF\) has no real force angle.
- When solving for force or lever arm, \(\sin\theta\) cannot be zero because the rearranged equation would divide by zero.
- When solving torque from power, shaft speed must be greater than zero; \(\tau=P/\omega\) is undefined at zero angular speed for nonzero power.
- At zero speed, a shaft can still carry torque, but its instantaneous rotational mechanical power \(P=\tau\omega\) is zero.
- Mass moment of inertia must be positive. When solving for \(I=\tau_{net}/\alpha\), torque and angular acceleration must use a consistent sign convention so the calculated inertia is positive.
Torque direction
In Force × Lever Arm mode, Advanced Options can report torque as magnitude only or apply a selected clockwise/counterclockwise sign convention when torque is the unknown. In Rotational Dynamics mode, signs come from the entered net torque or angular acceleration relationship. Keep one sign convention throughout a statics or dynamics problem.
Torque Units and Input Quality
The calculator converts each quantity to a consistent base unit before solving. That prevents unit-system mixing from changing the represented physical quantity, but the input still has to describe the correct force, distance, angle, power, inertia, or acceleration.
| Torque quantity | Equivalent | Use |
|---|---|---|
| 1 lbf·ft | 1.355818 N·m | Common U.S. customary torque unit |
| 1 lbf·in | 0.1129848 N·m | Useful for smaller torque values |
| 1 kgf·m | 9.80665 N·m | Uses standard gravity in the kilogram-force definition |
| 1 N·m | 0.737562 lbf·ft | Reciprocal of the lbf·ft conversion above |
Conversion basis: NIST Guide to the SI, Appendix B.9.
Measure distance from the axis
Use the distance from the pivot or rotation axis to the point of force application. If the force is angled, do not replace that distance with an assumed perpendicular distance unless you are intentionally using the moment-arm form.
Enter force, not mass
Newtons and pounds-force are force units. Kilograms and pounds-mass describe mass and require an acceleration relationship before they become force.
Match mechanical power to the shaft
Power mode uses mechanical shaft power at the same operating point as torque and speed. Electrical input power is not automatically equal to mechanical shaft output power.
Use inertia about the same axis
Moment of inertia depends on the selected rotation axis. A value about a center-of-mass axis cannot be substituted unchanged for a different parallel axis unless the appropriate transformation has been made.
Common Torque Mistakes and Edge Cases
Most surprising torque results can be traced to geometry, units, sign convention, or using a relationship outside the physical situation it represents.
| Problem | Why it happens | What to check |
|---|---|---|
| Torque is unexpectedly zero | The force angle is 0° or 180°, force is zero, or lever arm is zero. | Confirm the line of action and pivot location. |
| Angle cannot be solved | The requested torque magnitude is greater than \(rF\). | Increase force or lever arm, or lower the target torque. |
| Torque differs by a factor of 12 | lbf·ft and lbf·in were confused. | Remember 1 lbf·ft = 12 lbf·in exactly. |
| Motor torque seems too high | Speed may be too low for the stated power, or electrical input power may have been entered as shaft power. | Verify shaft RPM, mechanical output power, and the operating point. |
| Dynamics inertia is nonphysical | Net torque and angular acceleration were entered with inconsistent signs, or angular acceleration is zero while solving for inertia. | Use one rotational sign convention and a nonzero \(\alpha\) for \(I=\tau/\alpha\). |
Torque is not a bolt-preload calculator
Applying a torque to a wrench or fastener is a force-and-lever-arm problem, but converting tightening torque into bolt preload is a different engineering problem. Thread geometry, friction under the head or nut, lubrication, surface condition, fastener properties, and the specified tightening procedure can materially change clamp load. Use the actual fastener specification or an appropriate bolted-joint method for that task.
Assumptions and Limits
The equations are exact for their idealized variables, but a real mechanical system can require additional modeling. The calculator cannot determine whether a shaft, wrench, coupling, gear, bearing, fastener, or motor is adequately rated for the calculated load.
Force × Lever Arm
Assumes a defined pivot or axis, a known point of force application, and a known included angle. It calculates the moment produced by that force; it does not model deformation, contact changes, impact, frictional slip, or multiple unentered forces.
Power, Torque & RPM
Uses mechanical power and rotational speed at the same shaft and operating point. It does not infer motor efficiency, gearbox efficiency, starting torque, transient peaks, thermal limits, or a full speed-torque curve.
Rotational Dynamics
Uses the fixed-axis relationship \(\tau_{net}=I\alpha\). The moment of inertia must refer to the same axis as the angular acceleration, and torque must be the net torque about that axis.
Final design decisions
For equipment or safety-related use, compare the calculated demand with applicable manufacturer ratings, load cases, duty cycle, material limits, joints, supports, and the current design requirements governing the actual system.
How the calculation was checked
The force-angle relationship, net-torque relationship, rotational power equation, and fixed-axis dynamics equation were checked against OpenStax University Physics Volume 1, Chapter 10. U.S./SI force, length, inertia, and torque conversions used by the calculator were checked against NIST Guide to the SI Appendix B.8 and Appendix B.9.