What next?
Torque is rotational force. These are its linear and structural cousins.
How to use this calculator
- Enter the force applied.
- Enter the lever length and angle to the lever.
- Read the torque in newton-metres.
What your result means
Torque is the turning effect of a force — force times lever length times the sine of the angle, in newton-metres. A longer spanner needs less force for the same torque, and you get the most turning effect pushing at 90° to the lever.
Why this one is different
Only the part of your force acting across the arm does any turning, so the working states what percentage of it that is at the angle you entered. Pull straight along the arm and the answer is zero rather than force times radius, with a line explaining why — the failure that makes people think the tool is broken.
Why a longer spanner loosens a stubborn bolt
Torque isn’t just force — it’s force multiplied by distance from the pivot. That’s why a longer wrench frees a seized bolt your bare hands never could: you’re not stronger, you’ve got more leverage.
From bike pedals to engine specs to that flat-pack furniture, understanding torque explains a surprising amount of the mechanical world around you.
How it works
Torque is the turning effect of a force. It grows with both the size of the force and how far from the pivot it's applied. A force applied at 90° to the lever produces maximum torque; applied straight along the lever (0°) it produces none.
Formula
Example
200 N on a 0.3 m spanner at 90°:
Two ways to read that number. Halve the spanner to 0.15 m and you need 400 N — twice the effort — for the same 60 N·m. Keep the 0.3 m spanner but pull at 45° instead of square-on and you only deliver 200 × 0.3 × sin 45° = 42.4 N·m, a 29% loss for the same muscle.
Frequently asked questions
Why does angle matter?＋
Only the component of force perpendicular to the lever creates rotation. The sine term captures this, peaking at 90°.
Is N·m the same as a joule?＋
Dimensionally yes, but they describe different things — torque is a rotational effect, a joule is energy. They aren't interchangeable in practice.
Why do spec sheets quote lb-ft instead of newton-metres?＋
Pound-feet are the imperial equivalent, still standard in US workshop manuals. One newton-metre is 0.7376 lb·ft, so 60 N·m is about 44.3 lb·ft. Multiply N·m by 0.738 to get lb·ft, or divide by that to go back.
Why do bolts have torque specifications?＋
Torque is a proxy for the clamping tension in the bolt, which is what actually holds a joint together. Too little and the joint works loose; too much and the bolt yields.
How do friction and lubrication affect the figure?＋
Enormously. Most of the applied torque is consumed by friction under the head and in the threads, so a lubricated bolt reaches far higher tension at the same torque. Always use the spec that matches the condition, dry or lubricated.
How does a torque wrench extension change the setting?＋
Anything that lengthens the effective lever arm changes the torque at the fastener, so a crow-foot adapter fitted in line needs the wrench setting recalculated. Fitting it at 90 degrees to the handle leaves the arm unchanged.
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Assumptions & limitations
Engineering formulas are exact; the situations they model are not. Read your result with these limits in mind:
- Assumes a rigid lever and a force applied at a single point — a real spanner flexes slightly and a hand grips over a length.
- The angle is measured between the force and the lever arm. At 0° or 180° the torque is zero, however large the force.
- Gives applied torque only. It does not account for the friction or thread pitch that determine the clamping force a bolt actually achieves.
- Torque in N·m and energy in joules are dimensionally identical but physically different quantities — do not treat them as interchangeable.