Torque Calculator – Compute Moments, Force & Lever Arm Easily

Welcome to our advanced torque calculator, designed for engineers, technicians and hobbyists alike. Whether you’re calculating the twist applied to a shaft, designing a lever system, or verifying loading on a rotor, this tool helps you compute torque (τ), required force (F) or lever arm length (r) based on the classic formula τ = r × F × sin θ. Covering SI and imperial conversions, you’ll get rapid, reliable results.

What is Torque?

In mechanics, torque (also called moment of force) is the rotational equivalent of a linear force. It measures how much a force acting at a distance from a pivot causes an object to rotate. Formally, the magnitude of torque is τ = r F sin θ, where r is the lever arm (distance to pivot), F is the magnitude of the force applied, and θ is the angle between F and the lever arm vector. (Wikipedia – Torque)

Why Use a Torque Calculator?

Manual calculations risk unit errors (N·m vs. lbf·ft), incorrect angle factors, or forgetting to convert lever arms. The torque calculator addresses these issues by offering mode-selection (torque, force, lever arm), angle input, and automatic conversion to common units. Great for mechanical design, welding fixtures, bolted connections, motor shafts, robotics and more.

The Formula and Its Variants

τ = r × F × sin θ  
F = τ ÷ (r × sin θ)  
r = τ ÷ (F × sin θ)  
Units: τ in N·m (SI), or lbf·ft / lbf·in (imperial)
  

If θ = 90°, sin θ = 1 and formula simplifies to τ = r × F. For non-perpendicular forces, the sine factor reduces effective lever arm. For example, when a force is applied at angle 30° to the lever arm, sin 30° = 0.5, meaning only half the force contributes to torque. (Study.com – How to Calculate Torque)

Practical Applications

• Wrench & bolt torque: determining required force at a given wrench length.
• Motor shaft design: torque required for given power and speed, or verifying motor output.
• Lever systems: calculating required lever length for a given applied force and desired torque.
• Robotics & gear trains: verifying that output shafts, bearings and couplings are rated for applied moment.

How to Use the Torque Calculator: Step-by-Step

1. Choose calculation mode: “Calculate Torque”, “Calculate Force” or “Calculate Lever Arm”.
2. Enter values:
   • Torque (τ) in N·m (if needed)
   • Force (F) in N
   • Lever arm (r) in m
   • Angle θ in degrees (default 90° if perpendicular).
3. Click “Calculate” and get the result. If calculating torque, you’ll also see conversions to lbf·ft and lbf·in.
4. For reset, click “Reset”.

Worked Exercise

Example 1 – Open a heavy lid: You apply a force of 150 N at the end of a lever that is 0.4 m long, and the force is perpendicular to the lever (θ = 90°). τ = r × F × sin θ = 0.4 ×150×1 = 60 N·m. The torque calculator confirms 60 N·m (≈44.25 lbf·ft).

Example 2 – Bolt tightening with angle: A wrench is 0.3 m long, you apply force at 30° to the lever (θ = 30°) of 200 N. τ = 0.3×200×sin 30° = 0.3×200×0.5 = 30 N·m.

Unit Conversions & Imperial Systems

SI uses N·m for torque. In the U.S., common units are lbf·ft and lbf·in. Conversion factors: 1 N·m ≈ 0.73756 lbf·ft; 1 N·m ≈ 8.85074 lbf·in. (Wikipedia – Torque) Many torque specs are listed in lbf·ft; ensure you convert correctly when designing equipment or specifying tools.

Tips & Common Pitfalls

• Forces not perpendicular to lever reduce torque: always check angle θ.
• Lever arm must measure from pivot axis to line of action of force — not simply physical length of lever.
• When calculating motor torque from power and speed: T = P ÷ ω (rad/s) — convert RPM to rad/s: ω = RPM × 2π/60.
• Many specs specify torque at bolt or shaft — account for gear ratios or mechanical efficiency when designing overall system.
• Always record units clearly — mixing N·m with lbf·ft can cause big mistakes.

Related Tools

• Force Calculator
• Lever Arm Calculator
• Work & Energy Calculator
• Mechanical Power Calculator

Sources: Wikipedia – Torque • LibreTexts – Torque Tutorial • Study.com – How to Calculate Torque

Disclaimer: This torque calculator is for educational and estimation purposes only. For precision mechanical design, always verify with full media, bearing, gear and friction specifications.