Calculator
Formula Used
Lever Arm Model
N = τ / (r × sin θ)
Use this when a force acts at radius r and angle θ. A right angle gives the strongest torque effect.
Fastener Preload Model
N = τ / (K × d)
Use this approximation for bolt tightening. K is the nut factor and d is nominal diameter.
Friction Contact Model
N = τ / (μ × Rm × z)
Use this for clutches, pads, or friction interfaces. μ is friction, Rm is mean radius, and z is active surfaces.
All calculations convert inputs to base SI values first, then convert the final normal force into your chosen output unit.
How to Use This Calculator
- Select the model that matches your physical setup.
- Enter torque and choose its unit.
- Enter the needed geometry value and its unit.
- For lever mode, enter the force angle.
- For fastener mode, enter the nut factor.
- For friction mode, enter friction coefficient and active surfaces.
- Choose the force unit and decimal precision.
- Press calculate to show the result above the form.
- Use the export buttons to save CSV or PDF output.
Example Data Table
| Model | Torque | Geometry | Extra Inputs | Normal Force |
|---|---|---|---|---|
| Lever arm | 120 N·m | r = 0.25 m | θ = 90 deg | 480.0000 N |
| Lever arm | 90 N·m | r = 0.30 m | θ = 60 deg | 346.4102 N |
| Fastener preload | 60 N·m | d = 12 mm | K = 0.20 | 25,000.0000 N |
| Friction contact | 30 N·m | Rm = 60 mm | μ = 0.35, z = 2 | 714.2857 N |
Practical Notes
Torque and normal force are connected by geometry, friction, and assumptions. In a simple lever, a longer radius lowers the needed force. In a bolt, the same torque can create very different clamp force when lubrication changes the nut factor. In a friction contact, higher friction or more active surfaces reduces the required normal force for the same torque target.
Use the lever model when the force line and pivot geometry are known. Use the fastener model for approximate bolt preload checks. Use the friction model for clutch, brake, or pad style interfaces where torque is resisted through surface contact.
For design work, compare this estimate with test data, manufacturer guidance, or a more detailed mechanics model. Real systems can include thread losses, deformation, uneven loading, and changing friction conditions.
FAQs
1) What does this calculator solve?
It converts applied torque into estimated normal force using a lever, fastener preload, or friction contact relationship.
2) Which model should I choose?
Choose lever for direct rotation geometry, fastener preload for bolt tightening estimates, and friction contact for clutch or pad style interfaces.
3) Why does angle matter in the lever model?
Only the perpendicular component creates torque. A smaller angle lowers the effective moment arm and raises the needed normal force.
4) Is the fastener result exact?
No. Bolt preload from torque is an approximation because lubrication, thread condition, surface finish, and assembly practice change the nut factor.
5) What is the nut factor K?
It is an empirical tightening factor used in torque-preload estimates. Common values often range near 0.15 to 0.25.
6) What is the mean radius in friction mode?
It is the effective contact radius where the normal force produces resisting torque. Use the correct mean value from your geometry.
7) Can I export the result?
Yes. After calculation, use the CSV button for spreadsheet use or the PDF button for a simple printable report.
8) Why are there several output units?
Different industries use newtons, kilonewtons, or pounds-force. The calculator keeps one physics result and converts it for easier reporting.