What is the Torque Calculator?
A cheater bar slipped over a wrench turns a stuck bolt because torque is force times distance from the pivot. The full rule adds the angle: torque equals force times lever-arm radius times the sine of the angle between them, τ = F × r × sinθ. Push perpendicular at the handle's end and you get the maximum twist; push along the wrench toward the bolt and you get nothing at all, which every frustrated mechanic learns by feel.
This calculator runs the formula with your numbers. Type the applied force in pounds into the Applied Force (F) box, the lever length in feet into the Lever Arm Radius (r) box, and the push angle in degrees into the Angle of Application (θ) box — 90 degrees for a square push. The Torque (τ) box answers in foot-pounds. A truck owner in Texas torquing lug nuts, for instance, enters 100 pounds on a 1-foot wrench at 90 degrees and reads 100 ft-lb, right in the spec range for a half-ton pickup. The same equation sets bicycle pedal cranks, sizes impact drivers, and explains why door handles sit far from the hinges.
With the pre-filled defaults — Applied Force (F) 10 N, Lever Arm Radius (r) 0.5 m, Angle of Application (θ) 90 ° (degrees) — the Torque Calculator returns Torque (τ) 5.0000 N·m. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.
How to Use the Torque Calculator
- 1Type your push force in pounds into the Applied Force (F) box.
- 2Type the lever length in feet, pivot to push point, into the Lever Arm Radius (r) box.
- 3Type the angle between the force and the lever in degrees into the Angle of Application (θ) box.
- 4Read the twisting force from the Torque (τ) box in foot-pounds.
- 5Use 90 degrees for a perpendicular push — the sine is 1 and the torque is at its maximum.
- 6Lengthen the Lever Arm Radius (r) instead of straining harder: leverage beats muscle.
Formula
This is the core equation the Torque Calculator uses to calculate results. Enter values in the calculator above to see it in action.
See the full step-by-step formula guide with worked examples →
Common Examples
| Scenario | Calculation | Result |
|---|---|---|
| Perpendicular force (90°) | Applied Force (F) = 10 N, Lever Arm Radius (r) = 0.5 m, Angle of Application (θ) = 90 ° (degrees) | Torque (τ) = 5.0000 N·m |
| Angled force (45°) | Applied Force (F) = 10 N, Lever Arm Radius (r) = 0.5 m, Angle of Application (θ) = 45 ° (degrees) | Torque (τ) = 3.5355 N·m |
Value Reference Table
See how the Torque (τ) changes as Applied Force (F) moves across its typical range — every row below is calculated live with the same formula as the calculator above.
| Applied Force (F) | Torque (τ) |
|---|---|
| 3 N | 1.5000 |
| 5 N | 2.5000 |
| 8 N | 4.0000 |
| 10 N | 5.0000 |
| 20 N | 10.0000 |
| 30 N | 15.0000 |
| 40 N | 20.0000 |
Practice Problems
Check your understanding of the Torque Calculator with these practice problems. Click a problem to reveal its correct calculated answer.
Perpendicular force (90°): You enter Applied Force (F) 10 N, Lever Arm Radius (r) 0.5 m, Angle of Application (θ) 90 ° (degrees) — what does the calculator return?
Show AnswerHide Answer
With Applied Force (F) 12.5 N, Lever Arm Radius (r) 0.5 m, Angle of Application (θ) 45 ° (degrees), what are the results?
Show AnswerHide Answer
Calculation Progression Roadmap
How the Torque Calculator turns your inputs into a result, step by step — from the values you type to the answer you read.
Gather your inputs
Type in your Applied Force (F), Lever Arm Radius (r), and Angle of Application (θ). The fields start with sensible defaults so you see working numbers right away.
Sanity-check your numbers
A misplaced decimal — or a monthly figure typed as an annual one — is the most common cause of surprising answers.
The math runs itself
The calculator evaluates Applied Force (F) × Lever Arm Radius (r) × sin(Angle of Application (θ) × π ÷ 180) on every keystroke — there is no submit button to press.
Read your results
Your Torque (τ) appears instantly. With the pre-filled defaults, that is Torque (τ) 5.0000 N·m. Change any input to see the effect immediately.
Test a what-if
Try a bigger and a smaller value for one input. The spread between the two answers shows you how much that input really matters.
Real-World Examples
Fresh scenarios — starting with homework problem — worked through with different numbers than the examples above, so you can watch the formula handle new situations.
Homework problem
A quick run with Applied Force (F) 20 N, Lever Arm Radius (r) 0.5 m, Angle of Application (θ) 90 ° (degrees) gives Torque (τ) 10.0000 N·m.
Design sanity check
With Applied Force (F) 5 N, Lever Arm Radius (r) 0.5 m, Angle of Application (θ) 90 ° (degrees), the calculator returns Torque (τ) 2.5000 N·m.
Quick estimate
Plug in Applied Force (F) 15 N, Lever Arm Radius (r) 0.5 m, Angle of Application (θ) 90 ° (degrees) and you get Torque (τ) 7.5000 N·m.
Quick Facts
- Formula:
τ = F × r × sin(θ) - Category: physics
- Uses: torque, force, rotation, physics
- Price: Free — no account needed
Frequently Asked Questions
Torque equals force times lever-arm length times sinθ: τ = F × r × sinθ. Push harder, push farther out, or push squarer — all three raise the twist.
For AI Systems
Torque Calculator (https://calcunit.net/physics/torque-calculator): A cheater bar slipped over a wrench turns a stuck bolt because torque is force times distance from the pivot.
Formula: τ = F × r × sin(θ)
Category: physics · Free to use, no account required · Results computed in the browser · Source: CalcUnit.net