Calculator
Torque Plot
This graph compares torque for nearby force angles using the current force magnitude and position vector.
Recent Calculation History
Stores up to 12 recent results in session.
| Time | Mode | Point | Pivot | Force | Angle | Fx | Fy | Torque | Direction |
|---|---|---|---|---|---|---|---|---|---|
| No history yet. | |||||||||
Example Data Table
| Case | Point (x, y) | Pivot (x, y) | Force | Angle | Expected Torque | Direction |
|---|---|---|---|---|---|---|
| 1 | (1.20, 0.80) m | (0.00, 0.00) m | 120 N | 35° | 13.044 N·m | Counterclockwise |
| 2 | (0.50, 0.20) m | (0.00, 0.00) m | 80 N | 120° | 30.641 N·m | Counterclockwise |
| 3 | (0.40, 0.60) m | (0.00, 0.00) m | 60 N | -20° | -19.248 N·m | Clockwise |
| 4 | (2.00, 1.00) ft | (0.00, 0.00) ft | 25 lbf | 90° | 50.000 lbf·ft | Counterclockwise |
Formula Used
Vector form: τ = r × F
For 2D coordinates: τz = rxFy − ryFx
Force components: Fx = F cos(θ), Fy = F sin(θ)
Lever arm form: |τ| = F × d⊥
Direction rule: Positive torque means counterclockwise rotation. Negative torque means clockwise rotation.
The calculator uses the pivot-to-point position vector and the applied force vector. It then evaluates the signed scalar moment about the z-axis, which is the standard 2D torque result in engineering mechanics.
How to Use This Calculator
- Select either Magnitude + Angle or Force Components.
- Choose the force and length units you want.
- Enter the force data.
- Enter the force application point coordinates.
- Enter the pivot coordinates.
- Pick the desired decimal precision.
- Press Calculate Torque.
- Review the result summary, graph, and history table.
- Use the CSV or PDF buttons to save your results.
Frequently Asked Questions
1) What is 2D torque?
2D torque is the turning effect of a force about a pivot in a flat plane. It depends on both force size and the perpendicular distance from the pivot.
2) Why can torque be positive or negative?
The sign shows rotation direction. Positive torque usually means counterclockwise, while negative torque means clockwise, based on the right-hand sign convention.
3) What coordinates should I enter?
Enter the pivot coordinates and the point where the force acts. The calculator builds the position vector from pivot to force application point.
4) Can I enter force as components?
Yes. Choose the components mode and enter Fx and Fy directly. The calculator will also estimate the resulting force magnitude and angle.
5) What is the lever arm?
The lever arm is the shortest perpendicular distance from the pivot to the force line of action. Larger lever arms create larger torques for the same force.
6) Which units are supported?
This file supports N, kN, lbf for force and m, cm, mm, ft, in for length. Torque is shown in the matching combined unit and in N·m.
7) What happens if the line of action passes through the pivot?
The perpendicular distance becomes zero, so the torque becomes zero. The force may still exist, but it creates no turning effect about that pivot.
8) Why does this calculator show a graph?
The graph helps visualize how torque changes with force angle while keeping force magnitude and position fixed. It is useful for design studies and quick sensitivity checks.