Torque Calculator

Torque Calculator for lever arm torque, shaft torque from power and rpm, and torque from I and α. It also solves for force, arm or angle, and adds up net torque on a lever or beam.

What the Torque Calculator Solves

The Torque Calculator covers the four ways torque shows up in physics and in the shop. Pick a case in the Calculate menu and only the inputs for that case appear, so an engine problem never asks for an angle and the speed field stays optional in the lever modes.

Every mode gives the main answer with the working written out underneath it. Four result cards add the figures people usually need next, such as the same torque in lbf·ft and kgf·m, the hand force at common wrench lengths and the shaft power at a set speed.

Torque Formula and Lever Arm

Torque is the turning effect of a force about a pivot. It grows with the size of the force, with the distance from the pivot to where the force acts, and with how square the force is to the arm. The general formula from OpenStax University Physics, section 10.6 is the one the AI Overview quotes.

$$\tau = r F \sin\theta$$

Here τ is torque in N·m, r is the lever arm from the pivot to the point where the force acts, F is the force and θ is the angle between the arm and the force line. When the push is square to the arm, sin 90° = 1 and the short form τ = r × F applies.

The default example in the Torque Calculator is a 120 N push on a 0.5 m arm at 90°. That gives 0.5 × 120 × 1 = 60 N·m, which is 44.25 lbf·ft. Tilt the same push to 30° from the arm and sin 30° = 0.5, so the torque drops to 30 N·m with no change in effort.

Torque peaks at 90° and falls to zero at 0° and 180°, where the force points straight into or out of the pivot. That is why a door barely moves when you push near the hinge or push along its face. The Torque at Other Angles table under the results shows this drop from 0° to 90° for your own force and arm.

The three reverse modes rearrange the same equation. Use them when you know the torque spec and need the force, the handle length or the angle that delivers it.

$$F = \frac{\tau}{r \sin\theta}$$

$$r = \frac{\tau}{F \sin\theta}$$

$$\theta = \arcsin\left(\frac{\tau}{r F}\right)$$

The angle mode always has two answers, θ and 180° − θ, because both have the same sine. The calculator reports both, since pushing 30° above the arm or 30° below the far side of it gives the same turning effect. If the target is larger than r × F, no angle can reach it and the tool says so.

Force to Torque on a Wrench

A force to torque calculator is mostly used at the end of a wrench. With the angle left at 90°, enter the hand force and the distance from the bolt center to where your hand sits on the handle, not the full tool length. Gripping a 30 cm wrench at 25 cm means r = 0.25 m.

The third result card works the other way round. It shows the straight push needed at 15 cm, 25 cm and 45 cm handles to reach the torque on screen, which helps when judging a torque spec by feel or choosing a breaker bar for a stuck fastener.

Torque From HP and RPM

For engines and electric motors, the torque calculator from HP and the torque calculator from RPM are the same job. Power is torque times angular speed, so knowing any two of power, torque and speed gives the third. The speed must be in radians per second for the base formula.

$$\tau = \frac{P}{\omega}, \quad \omega = \frac{2 \pi n}{60}$$

Shop formulas fold the 2π and 60 into one constant. With power in mechanical horsepower and torque in lbf·ft the constant is 33,000 ÷ 2π ≈ 5,252, which is why hp and lbf·ft curves cross at 5,252 rpm on US dyno charts. With power in kW and torque in N·m it is 60,000 ÷ 2π ≈ 9,549.

$$\tau\,(\text{lbf} \cdot \text{ft}) = \frac{5252 \times P\,(\text{hp})}{n\,(\text{rpm})}$$

$$\tau\,(\text{N} \cdot \text{m}) = \frac{9549 \times P\,(\text{kW})}{n\,(\text{rpm})}$$

Torque in lbf·in uses 63,025 in place of 5,252, the figure motor sizing sheets often print. The tool skips these shortcuts and works in SI throughout, using the 745.7 W mechanical horsepower and the 735.5 W metric horsepower (PS) from NIST SP 811 Appendix B.9.

Engine Torque Example

Used as an engine torque calculator, the default case is 200 hp at 4,500 rpm. That speed is 471.2 rad/s, and 149,140 W ÷ 471.2 rad/s gives 316.5 N·m, or 233.4 lbf·ft. Check it with the shop formula and 5,252 × 200 ÷ 4,500 also lands on 233.4 lbf·ft.

The Torque at Other Speeds table holds the power fixed and halves or doubles the speed. It reads like a gearbox, because a 2:1 reduction doubles shaft torque and halves the speed while the ideal power stays the same.

Torque Calculator for a Car

A torque calculator for a car usually means one of two numbers. Engine torque at the crank comes straight from the power mode above. Torque at the wheels is engine torque multiplied by the gear ratio and the final drive ratio, then reduced by drivetrain losses, so it is several times larger than the crank figure in first gear.

$$\tau_{out} = \tau_{in} \times i \times \eta, \quad n_{out} = \frac{n_{in}}{i}$$

Open the Gearing panel in either power mode and enter the overall ratio i, which is the gear ratio times the final drive, plus the efficiency η. The third card then shows torque and speed at the output and the power left after losses.

With the default 3.5:1 ratio and 90% efficiency, the 233.4 lbf·ft engine example becomes 233.4 × 3.5 × 0.9 = 735.3 lbf·ft (996.9 N·m) at the output. The output turns at 4,500 ÷ 3.5 = 1,286 rpm, and the 149.1 kW from the engine drops to 134.2 kW after the 10% loss.

The same panel handles any gearbox or belt drive, not only cars. Set the ratio to 1 and efficiency to 100% for a direct drive, or use a ratio below 1 for an overdrive that trades torque for speed.

Torque Calculator for Cycling

Cyclists can use the same power mode with watts and cadence. A rider holding 250 W at 90 rpm puts 250 ÷ 9.425 rad/s = 26.53 N·m into the crank. Divide that by a 170 mm crank length and the average push square to the crank works out to about 156 N through each turn.

Motors work the same way. A 1.5 kW motor running at 1,450 rpm delivers 1,500 ÷ 151.8 rad/s = 9.88 N·m at the shaft, and the fourth card lists the same power in hp and PS for name plates written in other units. For quick power unit swaps on their own, the Watt Converter covers W, kW, hp and more.

Torque From Moment of Inertia

Newton’s second law for rotation links torque to how fast a body speeds up its spin. A body with a larger moment of inertia I needs more torque for the same angular acceleration α, just as a heavier cart needs more force for the same acceleration.

$$\tau = I \alpha$$

With the defaults of I = 0.5 kg·m² and α = 20 rad/s², the torque needed is 10 N·m. At that rate the body gains about 191 rpm each second, so it reaches 1,000 rpm in 5.24 s after about 43.6 turns. The first card shows these times and turns for the Target Speed you set under Units and Speed.

Find I for a disk, ring, rod or 20 other shapes with the Mass Moment of Inertia Calculator, and α from speeds and times with the Angular Acceleration Calculator. The energy the spinning body ends up holding comes from the Rotational Kinetic Energy Calculator.

A negative α means the torque opposes the spin, which is the braking torque a brake or a reversed motor must supply. With α = 0 the ideal torque is zero, though a real shaft still needs some torque to overcome bearing friction and air drag.

Net Torque and Balance

When several forces act on one beam, each makes its own torque about the pivot. By the usual sign convention, counterclockwise torques count as positive and clockwise ones as negative. Their sum is the net torque, and the beam only stays still when that sum is zero.

$$\tau_{net} = \sum r_i F_i \sin\theta_i \,(\text{ccw}) – \sum r_i F_i \sin\theta_i \,(\text{cw})$$

The default case is a seesaw with 392 N (about 40 kg) at 0.8 m on one side and 245 N (about 25 kg) at 1.2 m on the other. That gives 313.6 N·m counterclockwise against 294 N·m clockwise, so the net torque is 19.6 N·m and the heavier side wins.

The balance card then gives three single fixes. Moving F₂ out to 1.28 m, raising F₂ to 261.3 N, or moving F₁ in to 0.75 m each brings Στ back to zero. A third force can be added on either side from the Third Force panel.

Forces start square to the beam, but the Force Angles panel sets θ₁ and θ₂, and θ₃ sits in the Third Force panel. If F₂ pulls at 60° to the beam instead of 90°, its torque falls to 245 × 1.2 × sin 60° = 254.6 N·m. The net torque then grows to 59.0 N·m, and F₂ would have to move out to 1.48 m to balance.

The fourth card treats the forces as loads on the beam and counts only the part of each force that acts at 90° to it. With the default square forces, the pivot carries 637 N, about 65 kg, and the combined load acts 3.08 cm toward the F₁ side. For the straight-line version of the same idea, the Net Force Calculator adds forces rather than torques.

Torque Units and Conversion

The SI unit of torque is the newton-meter, written N·m. US specs use pound-force feet (lbf·ft, often shown as ft-lb) and pound-force inches for small fasteners, while older metric manuals use kilogram-force meters. The torque calculator converter card shows each result in the other systems using the NIST factors below.

• 1 lbf·ft = 1.355818 N·m, so 1 N·m = 0.7376 lbf·ft
• 1 lbf·in = 0.1129848 N·m, so 1 N·m = 8.851 lbf·in
• 1 kgf·m = 9.80665 N·m exactly, so 1 N·m = 0.10197 kgf·m
• 1 ozf·in = 0.007061552 N·m, used for small motors and servos
• 1 N·m = 1,000 N·mm = 1,000 mN·m, the units on small motor, servo and bolt data sheets

Searches like “20 nm in torque” or “1 nm in torque” mean newton-meters. Lowercase nm is the nanometer, a length, so torque should always be written N·m with a capital N. When someone asks how much 1 N·m of torque is in kg, they mean kgf·m, and the answer is 0.102 kgf·m or 10.2 kgf·cm.

The table turns common N·m figures into US and metric units. The last column is the straight push a hand must give at 25 cm from the bolt, about the grip point on a mid-size socket wrench, to reach that torque.

Pick any of the ten torque units under Units and Speed and every card, table and step updates to it. Force, length, power, speed, inertia and acceleration fields each carry their own unit menu, so mixed inputs such as pounds-force on a centimeter arm need no hand conversion.

How Much Torque Is That?

A torque number only has meaning next to the job. For hand work, the useful test is the force it takes at a given handle length. For engines and motors, torque needs a speed beside it before it says anything about power.

Take 40 N·m by hand. At a 25 cm grip it takes 160 N of steady pull, about the weight of a 16 kg mass, which is a firm two-handed effort for most people on a short wrench. At a 45 cm breaker bar the same 40 N·m needs only 89 N, which is why longer handles make stubborn bolts easier.

Is 10 N·m a lot of torque? At a 20 cm grip it is a 50 N push, the weight of about 5 kg, so it feels light on a hand tool. On a small electric motor it can be a lot, since 10 N·m at 1,450 rpm already means about 1.5 kW of output.

Whether 75 N·m is good depends on the speed it comes with. At 3,000 rpm it means 23.6 kW (31.6 hp), and at 6,000 rpm it doubles to 47.1 kW. In the same way, 300 N·m at 4,000 rpm is 125.7 kW, or 168.5 hp, and 400 N·m equals 295 lbf·ft. Run any of these in the Power from Torque and RPM mode to see the figure at your own speed.

Bolt Torque vs Lever Torque

A bolt torque calculator answers a different question from this one. It estimates the tightening torque T needed to stretch a bolt to a target clamp force F, using the short-form relation from fastener design references such as eFunda’s torque and tension guide.

$$T = K D F$$

D is the nominal bolt diameter and K is the nut factor, which lumps together thread and under-head friction. A value near 0.2 is the common figure for dry, mid-size steel bolts, and lubricated threads give a lower K. As an example, an M12 bolt tightened to 30 kN of preload with K = 0.2 needs 0.2 × 0.012 × 30,000 = 72 N·m.

Once you have that spec, the lever modes here take over. Enter 72 N·m as the target torque with your wrench length to see the pull it needs, or enter your pull to see what handle length reaches it. Keep in mind that friction varies, so torque only estimates preload and is not a direct measure of clamp force.

Torque vs Force, Work and Energy

Force pushes or pulls in a straight line and is measured in newtons. Torque is that force acting at a distance from a pivot, so it adds a length and is measured in N·m. The same 100 N can make 10 N·m on a 10 cm arm or 50 N·m on a 50 cm arm.

Torque and energy share the same base units, yet they are not the same thing. Energy is written in joules, while torque stays in N·m because it is a twist, not work done. Work appears only when the torque turns through an angle in radians.

$$W = \tau \theta, \quad W_{turn} = 2 \pi \tau$$

So 60 N·m turning one full revolution does 2π × 60 = 377 J of work, the figure on the fourth card of the default case. For the stiffness side of the same idea, torque per radian of twist, see the Rotational Stiffness Calculator. The torque you set also changes a body’s spin over time, which the Angular Momentum Calculator tracks as L.

Torque Calculator FAQ

These answers cover the torque questions people search most, from basic definitions to measuring and applying torque in practice. Each uses the same formulas and unit factors as the calculator above.

What is torque in physics?

Torque is the rotational counterpart of force. A force changes how fast something moves in a line, and a torque changes how fast it spins about an axis. Its size is r × F × sin θ, and its direction follows the right-hand rule, which in flat problems reduces to clockwise or counterclockwise.

How do I calculate how much torque I need?

Start from what the torque must do. To hold or start a load on a lever, multiply the load force by its distance from the pivot. To spin a body up, multiply its moment of inertia by the angular acceleration you want. Then add margin for friction, since real bearings, seals and gears all take some torque before anything moves.

How is torque measured?

Fastener torque is set and checked with a torque wrench, which reads or clicks at a set value. Engine and motor torque is measured on a dynamometer that loads the shaft and reads the reaction. Rotary torque sensors on a running shaft measure the tiny twist of a calibrated element and convert it to N·m.

What are the types of torque?

Static torque acts without causing rotation, such as the twist on a seized bolt that has not yet broken free. Dynamic torque changes the rotation speed, such as an engine accelerating a flywheel. In engineering you also see drive torque, braking torque and the twisting load on a shaft called torsion.

Why is torque called torque?

The word comes from the Latin verb torquere, which means to twist or turn. According to the Online Etymology Dictionary, its use for a rotating force dates from 1882. The same root gives English words such as torsion, contort and distort.

What is another name for torque, and what is it short for?

Torque is also called the moment of a force, or simply a moment, especially in statics and structural work. Its usual symbol is the Greek letter τ (tau), while engineers often write T or M. In casual use people also say twisting force or turning force, though torque is not itself a force.

What is torquing, and how do you torque a bolt?

Torquing means tightening a fastener to a set torque value with a torque wrench. Set the wrench to the spec, pull at the handle grip square to the wrench, and apply a smooth steady pull until it clicks or reads the value. Jerking the handle overshoots the reading and can leave the bolt tighter than intended.

Where is torque used?

Torque is at work in every door, wrench, steering wheel, bicycle crank and electric motor. Car and motor makers list torque because it sets how hard a shaft can turn a load. Structural designers use moments to size beams, and physics courses use torque to study balance and rotation, often with problems close to the seesaw default case above.

For more tools on spin, speed and rotational energy, browse the Rotational Motion Calculators, including the Angular Velocity Calculator for turning rpm into rad/s and the Flywheel Energy Storage Calculator for stored energy in a spinning disk.