Torque Calculator

Calculate torque from applied force and moment arm (T = F × r) with SI and Imperial unit support.

Calculator

N
m

Example Result

Your result will appear here

The calculated result will appear here after you press Calculate.

Watch: M10 Bolt: 50 Nm or 37 Nm? Dry vs Oiled Threads

M10 Bolt: 50 Nm or 37 Nm? Dry vs Oiled Threads

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The same M10 class 8.8 bolt has two correct torque values: about 50 N·m with dry threads (K ≈ 0.20) and about 37 N·m with oiled threads (K ≈ 0.15). T = K × F × d: oil cuts thread friction, so tightening an oiled bolt to the dry value raises the clamp load from about 25 kN to about 34 kN, right at proof load.

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About the Torque Calculator

Torque is the rotational equivalent of linear force — it measures how much a force causes an object to rotate about a pivot or axis. The torque formula T = F × r states that torque equals the applied force multiplied by the perpendicular distance from the pivot point to where the force is applied, a distance known as the moment arm or lever arm. Engineers use torque calculations every day: selecting the right motor for a drive system, specifying torque wrench settings for bolted joints, designing shafts and couplings, and calculating the mechanical advantage of levers and gear trains. This calculator supports both SI units — Newtons and metres producing Newton-metres — and Imperial units — pound-force and feet producing pound-feet. It automatically converts your result across all common torque units so you can compare values or carry the figure into the next stage of your design.

How to Use the Torque Calculator

  1. 1

    Select your unit system — SI (metric) or Imperial.

  2. 2

    Enter the force applied in Newtons (SI) or pound-force (Imperial).

  3. 3

    Enter the moment arm — the perpendicular distance from the pivot to where the force acts.

  4. 4

    Press Calculate. The result is shown in all common torque units automatically.

Torque Calculator Examples

Frequently Asked Questions

What is torque?

Torque is the rotational equivalent of linear force. It measures the tendency of a force to rotate an object about an axis, pivot, or fulcrum. The greater the force and the longer the moment arm, the more torque is produced.

What is a moment arm?

The moment arm (also called lever arm) is the perpendicular distance from the axis of rotation to the line of action of the applied force. Increasing the moment arm increases torque without increasing the force — this is the principle behind long wrenches.

What are the SI units for torque?

The SI unit for torque is the Newton-metre (N·m). Larger systems may use kilonewton-metres (kN·m). In Imperial units, torque is measured in pound-feet (lb·ft) or pound-inches (lb·in).

How do I convert N·m to lb·ft?

Multiply Newton-metres by 0.7376 to get pound-feet. For example, 100 N·m × 0.7376 = 73.76 lb·ft. To convert lb·ft to N·m, divide by 0.7376 (or multiply by 1.3558).

What is the difference between torque and moment?

In practice, torque and moment are often used interchangeably. Strictly, "torque" refers to a twisting force that causes rotation along an axis (like a motor shaft), while "bending moment" refers to a bending force about a point in a beam or structure. Both use the same formula F × r.

How does torque relate to power?

Power equals torque multiplied by angular velocity: P = T × ω. If you know torque in N·m and shaft speed in RPM, use the Power Calculator to find shaft power in watts, kilowatts, or horsepower.

What is a typical motor torque value?

Small electric motors (fractional horsepower) produce around 0.1–10 N·m. Industrial motors range from 10 N·m to thousands of N·m depending on power rating and operating speed. Low-speed, high-torque motors used in conveyors or mixers can produce tens of thousands of N·m.

How do I calculate torque for a bolted joint?

Bolt tightening torque is often calculated using T = K × F_i × d, where K is the nut factor (typically 0.15–0.25), F_i is the desired clamping force (preload), and d is the nominal bolt diameter. The basic T = F × r formula applies when you know the wrench force and handle length.

By O.E. — Partner, chairman of the board and CEO of a metal products manufacturer for 21 years; the company exports to 45 countries.

Drafted with AI assistance; calculations checked against primary sources and tested with the site's own code. About FlowUtil

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How Torque Is Calculated

FlowUtil applies the fundamental torque relation T = F × r, where T is the torque, F is the applied force, and r is the perpendicular moment arm from the rotation axis to the line of action of the force. In SI units a force in newtons multiplied by a moment arm in metres gives torque in newton-metres (N·m); in Imperial units a force in pound-force multiplied by a moment arm in feet gives pound-feet (lb·ft). The result is converted across N·m, kN·m, lb·ft, and lb·in so the same figure can be carried into the next design step in whichever unit is needed.

The formula assumes the force is applied perpendicular to the moment arm. If the force acts at an angle θ to the arm, the effective torque is F × r × sin(θ); this calculator covers the common case where the force is applied at 90°, so sin(θ) = 1 and the full product contributes. The conversion factor 1 N·m = 0.737562 lb·ft is exact to the precision shown and derives from the defined relationships between newtons, pounds-force, metres, and feet.

SymbolMeaning
TTorque (N·m or lb·ft)
FApplied force, perpendicular to the arm (N or lbf)
rMoment arm — perpendicular distance from axis to force line (m or ft)

Torque in SI and Imperial Units

  1. 1SI: 500 N applied at a 0.25 m moment arm.

    T = F × r = 500 × 0.25 = 125 N·m

    T = 125 N·m · ≈ 92.20 lb·ft

    A 500 N push on a 0.25 m wrench produces 125 N·m of torque — a typical small servo or hand-tightened industrial joint. The same force on a 0.5 m arm would double the torque to 250 N·m, which is why longer wrenches loosen stubborn bolts more easily.

  2. 2SI: 2000 N applied at a 0.05 m motor shaft radius.

    T = 2000 × 0.05 = 100 N·m

    T = 100 N·m · ≈ 73.76 lb·ft

    A belt delivering 2000 N of tangential pull on a 50 mm pitch radius loads the shaft with 100 N·m of torque. Combined with the shaft speed, this figure feeds directly into the Power Calculator (P = T × ω) to size the motor.

  3. 3Imperial: 75 lbf applied at a 2 ft moment arm.

    T = F × r = 75 × 2 = 150 lb·ft

    T = 150 lb·ft · ≈ 203.37 N·m

    A 75 lbf pull on a 2-foot breaker bar gives 150 lb·ft — a common wheel-lug or large-bolt tightening range. Note the unit is pound-feet (lb·ft) for torque, distinct from foot-pounds (ft·lbf) used for energy; the numerical value is the same but the physical quantity differs.

Understanding the Result

The result is a rotational moment expressed in N·m (SI) or lb·ft (Imperial). Physically it represents the tendency of the applied force to rotate the object about the axis; a larger torque means more rotational effect for the same geometry. The four unit stats let you read the same torque in whichever convention a datasheet, standard, or colleague uses.

Torque alone does not determine whether a shaft or bolt will survive — it must be combined with geometry to find stress (torsional shear τ = T·r/J) or with angular speed to find power (P = T × ω). Treat the torque value as an input to those downstream checks rather than as a pass/fail number on its own.

The calculation assumes a perpendicular force and a rigid, frictionless moment arm. Real systems include bearing friction, shaft flexibility, and force components that are not perfectly tangential, all of which reduce the effective torque delivered to the load.

What T = F × r Assumes

  • Perpendicular forceThe formula uses the full F × r product, valid when the force acts at 90° to the arm. At an angle, multiply by sin(θ).
  • Rigid armThe moment arm is treated as rigid; deflection or elasticity in the lever reduces delivered torque.
  • No friction lossesBearing and pivot friction are not deducted; the result is the torque applied at the point of action, not necessarily the torque reaching the load.
  • Unit consistencySI inputs (N, m) and Imperial inputs (lbf, ft) are handled separately by the unit toggle — do not mix units within one calculation.

Where This Comes Up

Typical engineering situations where this calculation is needed.

  • Motor and drive sizingFind the torque a belt, chain, or gear delivers to a shaft so the motor and coupling can be selected.
  • Wrench and lever designDetermine the handle length or force needed to reach a specified tightening or loosening torque.
  • Shaft stress inputSupply the torque value to torsional-stress and shaft-diameter calculations.
  • Power calculationCombine the torque with rotational speed to compute shaft power in watts or horsepower.

Torque Mistakes on the Bench

  • Confusing torque and momentTorque is a twisting moment about a shaft axis; a bending moment acts to bend a beam. Both use F × r but describe different loading.
  • Mixing SI and Imperial unitsEntering newtons with feet, or pound-force with metres, gives a numerically wrong result. Use the unit toggle to keep a system consistent.
  • Using diameter instead of radiusr is the distance from the axis to the force line — for a shaft that is the radius, not the diameter. Halving a diameter gives the radius.
  • Confusing lb·ft and ft·lbfPound-feet (lb·ft) is torque; foot-pounds (ft·lbf) is energy. The numbers coincide but the quantities do not.

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