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Gear ratio calculator for robots

Count the teeth on the gear fixed to the motor (the driver) and the gear it turns (the driven) to get the gear ratio, the output speed, the approximate torque and how fast your robot will move.

  • Made forClass 6 to 12, robotics, diploma
  • Shows the workingEvery step, ready for your practical file
  • Instant answersResults change as you type

Gear ratio, speed and torque

Enter the teeth on the driver gear (on the motor) and the driven gear. For a gearbox with more stages, add a row for each pair.

Gear pairs (stages)

Friction always takes some torque; 100% gives the ideal figure.

To see how fast a robot on these wheels moves.

Reset

Result

Gear ratio3 : 1Speed goes down and torque goes up (a reduction).
Driver 12TDriven 36T
Gear ratio
3 : 1
Output speed
200 RPM
Output torque (approx.)
3 kg·cmideal, no friction
Robot speed
0.68 m/s2.45 km/h
Output direction
Opposite to the motor

Working

  1. Stage 1: 36 ÷ 12 = 3.
  2. Output speed = 600 RPM ÷ 3 = 200 RPM.
  3. Output torque ≈ 1 kg·cm × 3 × 100% = 3 kg·cm.
  4. Robot speed = RPM × π × diameter ÷ 60 = 200 × 3.1416 × 0.065 m ÷ 60 = 0.681 m/s.
  • Note: Torque is approximate: real gears lose some to friction, and a motor gives its rated torque only near stall. Check the motor's datasheet for its speed and torque.
  • Tip: Every pair of meshing spur gears reverses the direction. Add an idler gear between them to keep the original direction without changing the ratio.

What it works out

Understanding gear ratios

Gears trade speed for turning force, called torque. When a small gear drives a big one, the big gear turns more slowly but with more torque, which is how a small, fast motor can lift a robotic arm or push a robot up a ramp.

The ratio is the number of teeth on the driven gear divided by the number on the driver. For a gearbox, multiply the ratios of each stage. Every pair of meshing gears also reverses the direction of turning.

Formula and worked example

Working out gear ratios by hand

The calculator uses exactly these formulas. Write them in your notebook and check one answer by hand: it is the surest way to remember them.

The formula

  • Gear ratio = driven teeth ÷ driver teeth
  • Output speed = motor speed ÷ gear ratio
  • Output torque ≈ motor torque × gear ratio × efficiency
  • Robot speed (m/s) = output RPM × π × wheel diameter (m) ÷ 60
RPM
revolutions per minute
torque
turning force, in kg·cm or N·m (1 kg·cm ≈ 0.098 N·m)
efficiency
the share of torque left after friction (100% is the ideal)

Worked example

A 12-tooth gear driving a 36-tooth gear

  1. Gear ratio = 36 ÷ 12 = 3, written 3 : 1.
  2. A 600 RPM motor gives 600 ÷ 3 = 200 RPM at the output.
  3. A motor torque of 1 kg·cm becomes about 1 × 3 = 3 kg·cm (less after friction).
  4. On 65 mm wheels: 200 × 3.1416 × 0.065 ÷ 60 = 0.68 m/s, about 2.45 km/h.

Answer3 : 1, 200 RPM, about 3 kg·cm, 0.68 m/s

In projects and exams

How students use it

Driver and driven teeth to gear ratio, output speed, approximate torque and robot speed. Here is where it earns its place in a school year.

  • Line followers and robot cars

    Pick a ratio that gives a controllable speed, because a robot that is too fast overshoots the line.

  • Robotic arms and cranes

    More reduction gives more lifting torque at the cost of speed; see the trade before you build.

  • Wind and water models

    A windmill model gears up the slow blades to spin a small generator faster.

  • Clocks and winches

    Working models of clocks and lifts depend on large reductions over several stages.

Check your work

Common mistakes to avoid

These are the slips that cost marks in exams and burn out parts on the bench.

  1. Turning the ratio upside down

    The ratio is driven ÷ driver. 12 driving 36 is a 3 : 1 reduction (slower, stronger), not 1 : 3.

  2. Miscounting teeth

    Mark one tooth with a pen and count round to it, or count twice.

  3. Expecting free torque

    Friction takes some torque, and a motor only gives its rated torque near stall. Treat the figure as an estimate.

  4. Mixing tooth sizes

    Two gears mesh only if their teeth are the same size (the same module or pitch), whatever their tooth counts.

Questions

Questions about gear ratios

Stuck on a project or a sum? Ask the institute on WhatsApp.

Ask on WhatsApp
Does a bigger gear ratio make my robot faster?

No: a bigger reduction ratio makes the output slower and stronger. For more speed use a smaller ratio, a faster motor or bigger wheels, and check the robot can still climb and turn.

What is an idler gear?

A gear placed between the driver and the driven gear. It reverses the direction once more, so the output turns the same way as the motor, without changing the overall ratio.

What does 1:48 on a gear motor mean?

The motor has a gearbox inside that turns the output shaft once for every 48 turns of the motor: the speed is divided by 48 and the torque multiplied (minus friction).

What is torque in kg·cm?

The turning force of a 1 kg weight hanging 1 cm from the shaft. 1 kg·cm is about 0.098 N·m. A motor of 2 kg·cm can just hold 1 kg on an arm 2 cm long.

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