Gear Reduction Calculator: RPM & Torque

A gear reduction calculator works out the output speed (RPM) and output torque of a gear train when you enter the input RPM, input torque, and the gear ratio (or the number of teeth on the driving and driven gears). You get the reduced speed and the multiplied torque, which is exactly what you need when sizing a motor, gearbox, or conveyor drive.

Formula

The core formulas are simple:

• Output speed: N_out = N_in / i
• Output torque: T_out = T_in × i

Where:

• N_in = input speed (RPM, revolutions per minute)
• N_out = output speed (RPM)
• T_in = input torque (N·m or lb-ft)
• T_out = output torque (same unit as input)
• i = gear ratio, defined as (number of teeth on driven gear) ÷ (number of teeth on driving gear). For a multi-stage gearbox, multiply the individual stage ratios.

This assumes 100% efficiency. Real gears lose 1–3% per mesh due to friction, so actual output torque is slightly lower.

Worked Example

Using the defaults from the calculator:

• Input speed = 1750 RPM
• Input torque = 10 N·m
• Gear ratio = 5

Step 1 – Output speed: 1750 ÷ 5 = 350 RPM

Step 2 – Output torque: 10 × 5 = 50 N·m

So a 1750 RPM motor with 10 N·m of torque, through a 5:1 reduction, turns at 350 RPM and delivers 50 N·m at the output shaft.

When to Use a Gear Reduction Calculator

You need this whenever you’re matching a motor to a load that runs slower but needs more torque. Common situations:

• Conveyor belts – motor runs fast, belt needs slow speed and high pull.
• Robotics – servo or stepper motors often need a gearbox to increase torque for joints.
• Electric vehicles – wheel speed is much lower than motor speed.
• Wind turbines – rotor turns slowly, generator needs high speed (this is a speed increaser, but the math is the same).
• Mixers, winches, and lifts – heavy loads require torque multiplication.

The calculator tells you whether a given motor and gearbox combination will meet your speed and torque requirements before you buy parts.

How to Choose the Right Gear Ratio

Start with your required output speed and torque, then work backward:

1. Determine the load speed (RPM) and load torque (N·m or lb-ft) needed.
2. Choose a motor whose speed is higher than the load speed.
3. Divide motor speed by load speed to get the ratio.
4. Check that motor torque × ratio ≥ load torque (with a safety margin, usually 1.5–2×).
5. If the ratio is large (over 10:1), consider a multi-stage gearbox – a single pair of gears may be impractical.

Example: You need 100 RPM and 30 N·m. A 1750 RPM motor with 5 N·m torque gives ratio = 1750/100 = 17.5. Output torque = 5 × 17.5 = 87.5 N·m, which is more than enough. But 17.5:1 is high for one stage; a two-stage gearbox (e.g., 5:1 × 3.5:1) would be better.

Common Mistakes and Misconceptions

• Confusing ratio direction: A “5:1 reductionâ€� means the input turns 5 times for each output turn. The ratio in the formula is 5, not 0.2.
• Ignoring efficiency: Real gearboxes lose power. If you need exact torque, multiply by efficiency (e.g., 0.95 per stage).
• Mixing torque units: Keep everything in the same unit – N·m or lb-ft. Don’t mix them in one calculation.
• Forgetting inertia: This calculator gives steady-state speed and torque. During acceleration, you also need to overcome the load’s inertia, which requires extra torque.
• Assuming torque multiplication is free: It comes at the cost of speed – power (P = torque × angular speed) stays roughly constant.

Limits of the Simple Formula

The basic formula assumes ideal gears with no friction, no backlash, and no elasticity. In practice:

• Efficiency: Each gear mesh loses 1–3%. A worm gear can lose 50% or more.
• Backlash: The small gap between teeth can cause positioning errors in robotics and CNC machines.
• Inertia mismatch: For high-performance systems, the reflected load inertia should match the motor inertia for best response.
• Strength limits: The gear teeth themselves can break if torque exceeds their rating – the calculator gives the theoretical output, but the gearbox must be physically capable.

For initial sizing, the simple formula is fine. For final design, consult manufacturer data and consider dynamic loads.

Frequently Asked Questions

What is the difference between gear reduction and gear ratio?
Gear ratio is the ratio of teeth (driven ÷ driving). Gear reduction specifically refers to a ratio greater than 1, where output speed is lower than input. A ratio of 1:1 is not a reduction; a ratio less than 1 (e.g., 0.5) would be a speed increase.

How do I calculate gear ratio from teeth?
Count the teeth on the driven gear (the one connected to the output) and the driving gear (connected to the input). Divide driven by driving. For example, a 40-tooth gear driven by a 10-tooth gear gives 40/10 = 4, a 4:1 reduction.

What happens to power through a gear reduction?
In an ideal gearbox, power (speed × torque) stays constant. In reality, friction reduces output power by the efficiency factor. So you get more torque but less speed, and slightly less power overall.

Can I use this calculator for multi-stage gearboxes?
Yes. Multiply the individual stage ratios to get the total ratio, then use that as the input. For example, a 3:1 stage followed by a 4:1 stage gives a total of 12:1.

What units should I use for torque?
Any unit works as long as you’re consistent. The calculator uses N·m by default, but you can enter lb-ft – the output torque will be in the same unit. Just don’t mix N·m and lb-ft in the same calculation.

Why is my actual output torque lower than calculated?
Because of friction, heat, and gear mesh losses. For a typical spur gear stage, assume 95–98% efficiency. If you need a precise number, check the gearbox manufacturer’s efficiency curve.

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in rpm | Input speed | RPM | 1750 | 0
in t | Input torque | N·m | 10 | 0
in r | Gear ratio (driven/driving) | - | 5 | 0
out out_rpm | Output speed | RPM | rpm / r | 2
out out_torque | Output torque | N·m | t * r | 2