Torque Calculator
Compute torque, force, or lever arm distance for mechanical and engineering applications with consistent unit handling and clear step-by-step math.
Calculation Steps
Calculator Guide
Torque Calculator: From Force and Radius to Reliable Torque Values
Use this Torque Calculator to turn real-world inputs—force, lever arm, angle, speed, and power—into clean, code-aware torque values in N·m or ft·lbf. This guide walks through the equations, assumptions, and sanity checks so you can trust the numbers in design, troubleshooting, or lab work.
Quick Start: Using the Torque Calculator Without Getting Burned
The calculator is built around the classic torque relationships \(\tau = F\,r\,\sin(\theta)\) for static/lever problems and \(\tau = \dfrac{P}{\omega}\) for rotating machinery. Follow these steps to get reliable results.
- 1 Choose what you want to solve for in the calculator’s Solve For menu: torque \(\tau\), force \(F\), lever arm \(r\), or angle \(\theta\) if that mode is available.
- 2 Select the correct mode: Static / Lever for wrenches, levers and brackets, or Rotating for motors, shafts and gearboxes (torque from power and speed).
- 3 Enter your known values and check units carefully. Use N / kN with metres for SI, or lbf with inches/feet for imperial. The calculator will convert everything internally.
- 4 For static torque, make sure the angle is the angle between the force and the lever arm, not just some arbitrary geometric angle. A force perpendicular to the lever gives \(\sin(\theta) \approx 1\) and maximum torque.
- 5 Press Calculate. The main result is shown in the “Calculated Result” box, while the quick stats show useful derived values like equivalent force or percentage of rated torque.
- 6 Open the Steps panel to see how the calculator rearranged the equations and substituted your values. This is especially useful when documenting design checks.
- 7 Use the Share button to copy a URL with your inputs pre-filled so you can paste it into emails, design reports or issue trackers.
Tip: When in doubt, start with simple perpendicular-force cases \(\bigl(\theta = 90^\circ\bigr)\). If the calculated torque is already near the component’s limit, you know you have a problem.
Warning: The calculator computes ideal torque. It does not automatically include friction, backlash, dynamic loads, or safety factors. Always compare outputs with relevant codes, standards and manufacturer ratings.
Choosing Your Method: Static vs. Rotating Torque
The same word “torque” shows up in at least two different contexts: a wrench on a bolt and a motor driving a shaft. The calculator lets you work in both worlds; pick the method that matches your actual problem.
Method A — Lever / Wrench Torque
Use this when torque is produced by a force acting on a lever arm: hand tools, valve handles, brake pedals, or any static reaction check.
- Directly maps to the basic equation \(\tau = F\,r\,\sin(\theta)\).
- Excellent for hand calculations, lab exercises, and quick sanity checks.
- Lets you solve either for torque, required force, or lever length.
- Does not model speed, inertia, or transient events explicitly.
- Assumes load is quasi-static; shock loads require additional factors.
Static torque: \(\tau = F\,r\,\sin(\theta)\)
Method B — Rotating Torque from Power & Speed
Use this when you know motor power and rotational speed and need shaft torque for sizing couplings, keys or gear teeth.
- Matches how motors and gearboxes are normally specified (kW and rpm).
- Ideal for quick checks of shaft sizing and gear train loading.
- Works for both electric motors and engines as long as power is known.
- Requires accurate power or efficiency estimates; nameplate power is not always available at your operating point.
- Gives average torque; ignores torsional vibration and peak transients.
Rotating torque: \(\tau = \dfrac{P}{\omega}\), where \(\omega = 2\pi n\) (rad/s)
Method C — Target Torque for Bolted Joints
Use torque as a proxy for bolt preload when you have recommended torque ranges from a standard or manufacturer.
- Easy to implement in the field with a torque wrench.
- Great for repeatable assembly operations and QA checks.
- Torque–preload relationship is sensitive to friction and lubrication.
- Use only within published torque ranges; do not extrapolate blindly.
Approximate relationship: \(F_{\text{preload}} \approx \dfrac{\tau}{K d}\) with joint constant \(K\).
What Moves the Number: Key Torque Levers
Before tweaking numbers, it helps to see which inputs actually have leverage. The chips below summarise the main variables in the Torque Calculator and how they interact.
Torque grows linearly with \(r\). Doubling the lever arm halves the required force for the same torque. Watch units—mixing millimetres and metres is a common source of order-of-magnitude errors.
More force gives more torque, but human operators and material limits cap how high you can go. For hand tools, ergonomic comfort and slip risk usually matter before material strength does.
Only the component of force perpendicular to the lever generates torque. When \(\theta\) falls from \(90^\circ\) to \(30^\circ\), the torque drops by a factor of \(\sin(30^\circ)/\sin(90^\circ) = 0.5\).
For rotating systems, torque is inversely proportional to speed: \(\tau \propto P/n\). High-speed motors produce lower shaft torque for the same power, so gear reductions are used to step torque up.
Real systems have friction, windage and electrical losses. If your drive train is only 90 % efficient, the available load torque is \(0.9\,\tau_{\text{shaft}}\). The calculator can include a simple efficiency factor where appropriate.
Most standards require you to stay below an allowable torque or shear stress. The calculator can show utilisation (e.g. “76 % of allowable”) so you can see headroom at a glance.
Worked Examples
Example 1 — Hand Torque on a Valve Wheel
You’re sizing a valve operator. A technician can comfortably push with a force of about \(F = 180\ \text{N}\). The valve wheel radius is \(r = 0.25\ \text{m}\), and the force is applied nearly tangentially, so \(\theta \approx 90^\circ\).
- Force: \(F = 180\ \text{N}\)
- Lever arm: \(r = 0.25\ \text{m}\)
- Angle: \(\theta = 90^\circ\), so \(\sin(\theta) \approx 1\)
- Mode: Static / Lever
- Solve for: Torque \(\tau\)
Example 2 — Motor Torque from Power and Speed
A conveyor requires 120 N·m of torque at 150 rpm. You have access to a 5 kW motor. Can it handle the load at that speed, ignoring dynamic effects?
- Motor power: \(P = 5\ \text{kW} = 5000\ \text{W}\)
- Speed: \(n = 150\ \text{rpm}\)
- Mode: Rotating
- Solve for: Torque \(\tau\)
- Required load torque: 120 N·m
The calculator automates conversions and lets you test “what-if” cases—different rpm, reduced efficiency, or increased load torque—without redoing all of the algebra.
Common Layouts & Variations
Torque appears in many standard layouts. The table below shows how you might configure the Torque Calculator for typical engineering scenarios.
| Scenario | Use This Mode | Key Inputs | Pros | Watch Out For |
|---|---|---|---|---|
| Hand wrench tightening a bolt | Static / Lever | Force, lever length, angle (≈90°) | Simple, very intuitive; great for teaching. | Friction and lubrication dominate actual bolt preload. |
| Valve operator or handwheel | Static / Lever | Allowable operator force, wheel radius | Easy ergonomic checks; clear design documentation. | Don’t forget worst-case differential pressure across the valve. |
| Electric motor driving a pump | Rotating | Motor power, shaft rpm, efficiency | Matches datasheets; directly gives shaft torque. | Transient start-up torques may be much higher than steady-state. |
| Gear reducer output shaft | Rotating | Input power, output rpm, overall efficiency | Accounts for speed reduction and efficiency in one place. | Check gear ratings; don’t exceed allowable tooth contact stress. |
| Winch or hoist drum | Static / Lever or Rotating | Line pull, drum radius (or motor power & rpm) | Simple way to relate line pull to shaft torque. | Include dynamic amplification factors for shock loading. |
| Test rig applying known torque | Static / Lever | Calibrated weight, lever arm, angle | High accuracy if geometry and weight are well known. | Small angle errors can significantly affect calibration results. |
- Confirm that the chosen mode matches the physical problem (static vs. rotating).
- Group calculations by unit system to avoid mixed-unit mistakes.
- For any safety-critical item, cross-check with a hand calculation.
- Document assumptions (efficiency, safety factor, friction) alongside the result.
Specs, Logistics & Sanity Checks
Torque is rarely the only design constraint. How you select tools, drives, and components around your torque requirement is just as important as the number itself.
Selecting the Right Tool or Drive
- Torque wrenches: Choose a range where your required torque sits in the middle 50 % of the scale for best accuracy.
- Motors and gearboxes: Check both torque and speed ratings, plus service factors from catalogues.
- Couplings and shafts: Compare calculated torque to allowable torque and shear stress; include overload factors.
Data You Should Have on Hand
- Required operating torque and any documented peak or stall torques.
- Duty cycle (continuous, intermittent, start–stop) and ambient conditions.
- Relevant standards (ASME, API, ISO, local codes) governing your application.
Sanity Checks Before You Trust the Result
- Compare calculator output with “back-of-the-envelope” estimates using rounded numbers.
- Ask: if I halve the lever arm, does the required force double? If not, units may be off.
- For rotating systems, verify that power, torque and speed satisfy \(P \approx \tau \omega\) within rounding error.
Treat the Torque Calculator as a transparent companion to your engineering judgement. The steps and equations are visible so you can paste them into reports or calculations and show exactly how you arrived at a design decision.