Calculator inputs
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Example data table
These examples help validate expected trends. Higher torque increases force demand, while longer arms reduce it when angle remains unchanged.
| Torque | Lever Arm | Angle | Required Force | Comment |
|---|---|---|---|---|
| 120 N·m | 0.30 m | 90° | 400.00 N | Purely perpendicular loading. |
| 120 N·m | 0.50 m | 90° | 240.00 N | Longer arm lowers force. |
| 120 N·m | 0.35 m | 60° | 395.90 N | Angle reduces effective arm. |
| 85 lb·ft | 18 in | 75° | 63.45 lbf | Useful for hand-tool estimates. |
Formula used
Torque formula: T = F × r × sin(θ)
Rearranged for force: F = T / (r × sin(θ))
Where:
- T = torque
- F = applied force
- r = lever arm length
- θ = angle between the force direction and lever arm
When the angle is 90°, sin(θ) becomes 1, so the formula simplifies to F = T / r. Angles closer to 0° or 180° reduce turning effectiveness and increase required force.
How to use this calculator
- Enter the torque value and choose its unit.
- Enter the lever arm length and choose its unit.
- Enter the angle between the lever arm and force direction.
- Select the preferred output force unit.
- Press Calculate force to view the result above the form.
- Review the applied force, perpendicular component, and normalized checks.
- Use the chart to see how force changes with lever length.
- Download the result summary as CSV or PDF.
FAQs
1) What does this calculator solve?
It converts a known torque into the force needed at a chosen lever arm and angle. It is useful for wrench loading, fixture design, tooling checks, and maintenance planning.
2) Why does angle matter?
Only the perpendicular part of force creates turning effect. When the angle drops, the effective moment arm becomes smaller, so more applied force is needed to create the same torque.
3) What happens at 90 degrees?
That is the most efficient case. The full force acts perpendicularly, so the equation simplifies to torque divided by lever arm.
4) Can I use imperial and metric units together?
Yes. The calculator normalizes values internally, then converts the answer into your selected output unit. This helps compare shop data from mixed standards.
5) Why is force very high at small angles?
Small angles create a tiny sine value. That shrinks the effective turning distance, so the force must increase sharply to maintain the same torque.
6) Is the perpendicular force component the same as the applied force?
Only at 90 degrees. At other angles, the perpendicular component is smaller than the applied force because only part of the force produces rotation.
7) Can this help with wrench extension estimates?
Yes. You can test different lever lengths and instantly see how the required input force changes. It is helpful for ergonomic reviews and manual loading estimates.
8) Does this replace engineering verification?
No. It supports fast estimation and planning. Final engineering work should still check material limits, fastener guidance, safety factors, and real loading conditions.