Input values
Enter up to three angled forces
Leave unused force magnitude and distance fields blank.
Example data table
Use degrees measured counterclockwise from the positive horizontal axis.
| Force | Magnitude | Radial distance | Position angle | Force direction | Moment direction |
|---|---|---|---|---|---|
| Force 1 | 120 N | 0.50 m | 0° | 90° | Counterclockwise |
| Force 2 | 80 N | 0.30 m | 180° | 90° | Clockwise |
| Force 3 | 40 N | 0.25 m | 45° | 135° | Counterclockwise |
Formula used
τnet = Στi
τ is torque. r is radial distance from the pivot. F is force magnitude.
θF is the force direction. θr is the position angle. Positive torque is counterclockwise.
How to use this calculator
- Choose the pivot point used for the torque calculation.
- Enter the force magnitude and its force unit.
- Enter radial distance from the pivot to the force location.
- Enter the position angle and force direction in degrees.
- Repeat for additional loads, then select a result unit.
- Calculate and inspect individual moments before using net torque.
Understanding angled-force torque
Understanding rotational effect
Torque is the turning effect produced by a force. It depends on size, location, and direction. The pivot is the reference point for every result. Mark it before entering measured values. Draw a radial line from the pivot to the force location. Then draw the force direction. The angle between those lines controls the moment. Large forces may create little torque near pivots. A smaller force can create a larger moment farther away. Only the sideways force component produces rotation.
Angles and lever arms
The calculator uses distance and two angles. One angle locates the application point. The other angle gives the force direction. Their difference is the included angle used in the formula. A ninety-degree difference creates maximum torque. A zero-degree difference creates no torque. A one-hundred-eighty-degree difference creates no torque. The force then acts directly toward or away from the pivot. Use one angular reference throughout the calculation. The positive horizontal axis is a practical reference. Consistent angle entries prevent sign errors.
Combining several forces
Each entered force creates an individual signed moment. The calculator adds moments to find net torque. Counterclockwise is positive. Clockwise results are negative. A positive total suggests counterclockwise turning. A negative total suggests clockwise turning. A total near zero indicates rotational balance about the chosen pivot. It does not prove net force is zero. Linear acceleration can occur. Check horizontal and vertical force sums separately when required. Never add moment magnitudes without signs. Direction is essential for a correct total.
Units and precision
Torque needs compatible force and distance units. The calculator converts choices into standard values. Newton metres are used internally. Results may display in kilonewton metres, pound feet, or pound inches. Use precision that reflects the actual data. Small angle errors can change the perpendicular force component. This matters near zero degrees. Confirm that each distance reaches the actual force location. Confirm that every force direction matches the diagram. Labels reduce mistakes. Recheck the selected output unit before reporting your answer.
Practical checks
Inspect each result before accepting the total. Compare direction with your diagram. A surprising sign can reveal reversed angle reference. It can reveal an incorrect lever-arm direction. Test simple cases. A horizontal arm with an upward force creates counterclockwise torque. A horizontal arm with a downward force creates clockwise torque. A force aimed along its arm creates zero torque. These checks expose entry errors. Use this tool for learning and early design estimates. Apply safety factors for final equipment decisions.
Why the pivot matters
Changing pivots changes each radial line. The same force can create a different moment. Select the hinge, shaft, bearing, or contact point. A pivot may simplify unknown reaction forces. It may make a known force create zero torque. This helps with equilibrium work. Keep a labelled diagram beside the input values. State the selected positive rotation direction. State the torque unit with the final result. Review measurements before sharing calculations. Good torque work combines geometry, force data, and careful interpretation.
Frequently asked questions
1. What is torque?
Torque is the tendency of a force to rotate an object about a selected point or axis. It combines force magnitude, distance, and the angle between the force and radial line.
2. Which angle should I enter?
Enter both angles from the same reference direction. The position angle points from the pivot to the force location. The force direction follows the applied force arrow.
3. Why is clockwise torque negative?
This calculator uses the common planar convention: counterclockwise is positive and clockwise is negative. The convention is arbitrary, but it must remain consistent for every force.
4. Why can torque be zero with a large force?
Torque is zero when a force acts through the pivot or exactly along the radial line. In both cases, the perpendicular force component is zero.
5. Can I combine several forces?
Yes. Enter up to three loads. The calculator determines each signed moment and adds them to obtain the net torque around the chosen point.
6. Which distance should I use?
Use the radial distance from the pivot to where the force is applied. The calculator uses the entered direction angles to determine the required perpendicular effect.
7. Does this calculator handle three-dimensional forces?
No. This tool evaluates planar forces around one point. Three-dimensional problems require vector cross products and torque components about multiple axes.
8. Which torque unit should I choose?
Choose the unit used by your project or problem statement. The internal calculation uses N·m, then converts the final result to your selected display unit.
9. Does a force through the pivot create torque?
No. A force whose line of action passes through the pivot has no perpendicular offset. Its moment about that point is zero.
10. What does a zero net torque mean?
It means clockwise and counterclockwise moments balance around that pivot. Other unbalanced forces may still cause straight-line acceleration.
11. How can I improve accuracy?
Use consistent units and verify directions before design decisions.