Motor Torque Calculator
This motor torque calculator works two ways — from force & lever arm (τ = F × d × sin θ) or from power & RPM — with a gear ratio multiplier, a torque-vs-RPM chart, and AI insights on whether your output torque meets your application's needs.
Motor torque inputs
Choose how you want to calculate torque, then enter your values.
What is motor torque?
Motor torque is the rotational force a motor's output shaft can deliver — it determines how heavy a load the motor can turn, lift, or accelerate.
It can be found two equivalent ways, depending on what you know:
| When you know… | Formula |
|---|---|
| Force & lever arm | τ = F × d × sin(θ) |
| Power & RPM (metric) | τ (N·m) = P (kW) × 9549 ÷ RPM |
| Power & RPM (imperial) | τ (lb·ft) = P (HP) × 5252 ÷ RPM |
| With a gearbox | τ_output = τ_motor × gear ratio |
How the Motor Torque Calculator Works — The Formula
From force & lever arm:
τ = F × d × sin(θ)
From power & RPM:
τ (N·m) = P (kW) × 9549 ÷ RPM
τ (lb·ft) = P (HP) × 5252 ÷ RPM
With a gearbox:
τ_output = τ_motor × gear ratio (RPM_output = RPM_motor ÷ gear ratio)
- F
- Applied force
- d
- Lever arm / pulley radius
- θ
- Angle between force and lever arm
- P
- Mechanical power (kW or HP)
- RPM
- Shaft speed in revolutions per minute
- Gear ratio
- Output : input speed reduction (and torque multiplier)
Worked example (Force & Lever Arm): a 200 N force applied at 0.4 m from a pivot at 90° produces τ = 200 × 0.4 × 1 = 80 N·m. The same force at 45° produces τ = 200 × 0.4 × sin(45°) ≈ 56.6 N·m — 29% less torque for the same effort.
Worked example (Power & RPM): a 5 kW motor at 1500 RPM produces τ = 9549 × 5 ÷ 1500 ≈ 31.8 N·m at the motor shaft. Through a 10:1 gearbox, the output shaft delivers ≈ 318 N·m at 150 RPM.
How to Use the Motor Torque Calculator
- Choose a mode: From Force & Lever Arm if you know the force applied and the distance from the pivot, or From Power & RPM if you know your motor's power rating and shaft speed.
- Fill in the fields for your chosen mode — force, lever arm, and angle, or power and RPM.
- Enter a gear ratio if your motor drives a gearbox (use 1 for direct drive).
- Optionally enter the required torque for your application to get an instant pass/fail check.
- Click Calculate to see your results instantly.
- Scroll to the AI Insights section to understand what your result means.
How to Interpret Your Motor Torque Results
What a Good Result Looks Like
A good result is one where the output torque (after any gear ratio) clearly exceeds the torque your application actually needs — with a margin of roughly 20-50% to cover friction, acceleration, and efficiency losses that this idealised formula doesn't account for. If you entered a "Required torque" value and the AI Insights panel shows a pass with healthy headroom, your motor and gearbox combination is likely adequate.
Warning Signs in Your Results
Watch out for: an output torque that's lower than your required torque (the AI Insights panel will flag this explicitly); a gear ratio so high that the resulting output RPM becomes impractically slow for your application; or a torque value that seems too good to be true for a small, low-power motor — double check your power unit (kW vs HP) and that the gear ratio hasn't been double-applied.
How to Improve Your Result
If your output torque falls short: (1) increase the gear ratio — doubling it roughly doubles output torque (and halves output speed); (2) choose a higher-power motor, since torque scales linearly with power at a given RPM; (3) for force/lever-arm setups, increase the lever arm length or move closer to a 90° angle between force and lever, since sin(90°) = 1 gives maximum torque for the same force.
Motor Torque Calculator Examples
Calculate Motor Torque from Power and RPM
A 5 kW electric motor runs at 1500 RPM direct-drive (no gearbox). What torque does it deliver?
- Mode: From Power & RPM
- Power (P): 5 kW
- Shaft speed: 1500 RPM
- Gear ratio: 1 (direct drive)
Result: τ = 9549 × 5 ÷ 1500 ≈ 31.8 N·m (≈ 23.5 lb·ft).
What this means: at 1500 RPM, this motor can deliver about 31.8 N·m of continuous torque. What to do next: try changing the RPM to see how torque rises at lower speeds and falls at higher speeds for the same power — this is the torque-vs-RPM chart shown above.
Torque Required to Lift a Load Calculator
A winch needs to lift a 50 kg load using a drum with a 0.15 m radius. What torque is required at the drum?
- Mode: From Force & Lever Arm
- Force (F): weight = 50 kg × 9.81 m/s² ≈ 490.5 N
- Lever arm (d): 0.15 m (drum radius)
- Angle θ: 90° (cable pulls tangentially)
Result: τ = 490.5 × 0.15 × sin(90°) ≈ 73.6 N·m.
What this means: the drum needs at least 73.6 N·m to lift the load at constant speed (more to accelerate it). What to do next: enter 73.6 in the "Required torque" field along with a candidate motor's output torque (Power & RPM mode) to check it's sufficient.
DC Motor Torque vs Speed Calculator with Gear Ratio
A small DC motor produces 0.4 kW at 3000 RPM and drives a 10:1 reduction gearbox. What torque and speed are available at the gearbox output?
- Mode: From Power & RPM
- Power (P): 0.4 kW
- Shaft speed: 3000 RPM
- Gear ratio: 10
Result: motor-shaft τ ≈ 1.27 N·m → output torque ≈ 12.7 N·m at 300 RPM.
What this means: the gearbox trades a 10x reduction in speed for a 10x increase in torque. What to do next: compare the "Direct drive" vs "5:1" vs "10:1" rows in the scenario table to see this trade-off across different gear ratios.
Frequently asked questions
What is torque?
Torque (also called moment of force) is the rotational equivalent of linear force. It measures how effectively a force causes an object to rotate about an axis. Torque depends on three things: the magnitude of the force, the perpendicular distance from the axis to the line of action of the force (the lever arm), and the angle between them. Its SI unit is the newton-metre (N·m).
How is motor torque calculated?
There are two common approaches. From force and geometry: τ = F × d × sin(θ), where F is the applied force, d is the lever arm (e.g. pulley radius), and θ is the angle between them. From power and speed: τ (N·m) = P (kW) × 9549 ÷ RPM, or τ (lb·ft) = P (HP) × 5252 ÷ RPM. A 5 kW motor running at 1500 RPM produces about 9549 × 5 ÷ 1500 ≈ 31.8 N·m of shaft torque. If the motor drives a gearbox, multiply by the gear ratio to get the output torque.
What is the relationship between torque and RPM?
For a fixed power output, torque and RPM are inversely proportional: τ = P × 9549 ÷ RPM. Double the RPM and torque halves for the same power; halve the RPM and torque doubles. This is why low-RPM motors (and gearboxes that reduce speed) deliver much higher torque than high-RPM motors of the same power rating — the torque-vs-RPM chart in this calculator visualises that curve for your inputs.
How do I choose the right motor torque for my application?
Start from the load: calculate the torque actually required (e.g. force needed × lever arm/radius for lifting, or load torque for a conveyor). Then size a motor (and optional gearbox) so its output torque, after any gear reduction, comfortably exceeds that requirement — engineers typically apply a safety margin of 20-50% to account for friction, acceleration, and efficiency losses. Use the 'Required torque' field in this calculator to get an instant pass/fail check against your motor's output torque.
What units is torque measured in?
In SI, torque is measured in newton-metres (N·m). Other common units include kilonewton-metres (kN·m) for large civil engineering loads, pound-feet (lb·ft) and pound-inches (lb·in) in the imperial system, and kilogram-force metres (kgf·m) in older engineering texts. Note that N·m is dimensionally the same as joules (J), but torque and energy are different physical quantities — torque uses N·m while energy uses J to keep the distinction clear.
What is a moment arm?
The moment arm (also called lever arm or moment of force arm) is the perpendicular distance from the axis of rotation to the line of action of the force. When the force is not perpendicular to the lever, you must multiply by sin(θ) to get the effective moment arm. Maximising the moment arm — for example, applying force at the end of a long wrench, or using a larger pulley radius — maximises the torque for a given effort.
How does a gear ratio affect motor torque?
A gearbox trades speed for torque (or vice versa) at a fixed ratio. A 5:1 reduction gearbox multiplies the motor's output torque by 5 while dividing its output speed by 5 — ideally with no power loss (real gearboxes lose a few percent to friction). This calculator's gear ratio field applies that multiplier directly: enter 1 for direct drive, or the gearbox's reduction ratio (e.g. 5 for a 5:1 box) to see the torque available at the output shaft.
How does torque relate to tightening bolts and fasteners?
Torque wrenches measure the twisting force applied to a fastener. Over-tightening can stretch or snap the bolt; under-tightening can cause joints to loosen. Vehicle wheel nuts, cylinder head bolts, and structural fasteners all have manufacturer-specified torque values (e.g. 120 N·m) to achieve the correct clamping force without yielding the fastener. Use the "From Force & Lever Arm" mode to verify the force and lever arm combination needed to hit a target torque.