Calculator Inputs
Torque Angle Plot
The chart shows how torque changes with force angle while keeping force and lever arm constant.
Example Data Table
| Case | Force | Radius | Angle | Torque Formula | Torque Result |
|---|---|---|---|---|---|
| Valve Handle | 150 N | 0.25 m | 90 deg | 150 × 0.25 × sin(90) | 37.50 N·m |
| Drive Arm | 420 N | 0.18 m | 60 deg | 420 × 0.18 × sin(60) | 65.47 N·m |
| Wheel Lug Tool | 80 lbf | 12 in | 90 deg | 355.86 × 0.3048 × sin(90) | 108.48 N·m |
| Machine Lever | 1.2 kN | 0.50 m | 30 deg | 1200 × 0.50 × sin(30) | 300.00 N·m |
Formula Used
Main torque formula: τ = F × r × sin(θ)
Where:
τ= torqueF= applied forcer= lever arm radiusθ= angle between the force and lever arm
Tangential force: Ft = F × sin(θ)
Angular acceleration: α = τ / I
Angular velocity from RPM: ω = 2π × RPM / 60
Power: P = τ × ω
Rotational work: W = τ × φ
Positive torque is shown for counterclockwise rotation. Negative torque is shown for clockwise rotation.
How to Use This Calculator
- Enter the applied force and choose its unit.
- Enter the lever arm radius and choose the matching length unit.
- Provide the angle between the force and lever arm.
- Enter moment of inertia, speed, and rotation angle.
- Select the torque sign direction for clockwise or counterclockwise motion.
- Press Calculate Torque to view results above the form.
- Use the CSV or PDF buttons to export the calculated values.
- Review the chart to see how torque varies with angle.
Frequently Asked Questions
1. What is rotation torque?
Rotation torque is the turning effect created by a force acting at a distance from a pivot or shaft center. Larger force, longer radius, or a better angle increases torque.
2. Why does the angle affect torque?
Only the force component perpendicular to the lever arm produces turning action. That is why torque uses sin(θ). Torque is maximum at 90 degrees and zero at 0 or 180 degrees.
3. When is torque equal to zero?
Torque becomes zero when the force is zero, the lever arm is zero, or the force acts directly along the lever arm. In those cases, there is no perpendicular turning component.
4. Which units can I use here?
This calculator supports multiple force, distance, and inertia units. It converts all entries to standard SI values internally, then reports torque in N·m, kN·m, and lb-ft.
5. What does the direction option change?
The direction option assigns the torque sign. Counterclockwise is shown as positive. Clockwise is shown as negative. This helps when analyzing rotational equations and machine motion direction.
6. Why is moment of inertia included?
Moment of inertia links torque to angular acceleration. A large inertia resists rotational change more strongly, so the same torque produces less angular acceleration on a heavier or wider rotating body.
7. Why does shaft power depend on RPM?
Power measures how fast rotational work is delivered. For the same torque, higher angular velocity means greater power. That is why fast shafts can transmit high power even with moderate torque.
8. Can I use this for final machine design?
It is useful for fast engineering estimates, comparisons, and education. Final design should also include material strength, fatigue, safety factors, shock loading, bearing limits, and detailed system geometry.