Gear and Belt Ratios: The Same Trade, Two Ways

Gears and belts do the same job by different means: trade speed for torque, or the reverse. The arithmetic is the same shape in both, and the differences that matter are practical rather than mathematical.

Gears: teeth decide everything

Ratio is driven teeth over driver teeth, and it is simultaneously the speed divisor and the torque multiplier. From the gear ratio calculator:

• 20T driving 60T at 1,500 rpm with 10 N·m in → ratio 3, output 500 rpm, output torque 30 N·m.
• 40T driving 20T at 1,000 rpm with 25 N·m in → ratio 0.5, output 2,000 rpm, output torque 12.5 N·m.

The trade is exact and symmetrical: three times the torque costs exactly a third of the speed. Power is conserved, which is the underlying reason — and the calculator ignores losses, so real output torque is slightly lower than the figure.

Belts: diameters instead of teeth

Same relationship, with pitch diameters standing in for tooth counts. The belt and pulley calculator on a 100 mm driver to a 250 mm driven pulley at 1,450 rpm, 600 mm between centres:

• Ratio 2.5, driven speed 580 rpm
• Belt speed 7.59 m/s (455.5 m/min)
• Belt length 1,759.2 mm

Belt speed is the one people forget to check. It is the same everywhere along the belt and it is what determines whether a drive is running within the belt's rated range — too slow and you need excessive tension for the power, too fast and centrifugal effects and heat become the limit.

Choosing between them

The practical differences, none of which appear in the ratio:

• Slip. A friction belt can slip, which is sometimes a fault and sometimes a feature — it is a crude overload protection that a gear train does not offer. Toothed belts and chains do not slip, and neither do gears.
• Exact phase. If input and output must stay synchronised, a friction belt is unsuitable regardless of ratio.
• Centre distance. Belts and chains span distance cheaply; gears must mesh, so a long span needs an idler train or a different solution entirely.
• Noise, damping and shock. Belts absorb shock and run quietly; gears transmit it and are noisier. That is a real consideration on a drive with an intermittent load.
• Maintenance. Belts stretch and need tension adjustment and replacement; chains need lubrication and take up slack; gears need lubrication and are otherwise long-lived.

Stacking ratios

Large reductions rarely come from a single pair, because one enormous gear is impractical. Two stages of 3:1 give 9:1 overall, and the arithmetic simply multiplies — run the calculator twice, feeding the first output into the second input.

Worth remembering that torque multiplies at every stage while losses accumulate at every stage too, so a four-stage reduction delivers noticeably less than the ideal figure.

Where the numbers stop

These calculators give kinematics: what speed and what torque, ignoring losses. They say nothing about whether a gear tooth or a belt can actually carry the load — that is a strength and rating question involving face width, material, belt section, wrap angle and service factor, and it is where an actual drive gets designed.

Use the ratio arithmetic to size the concept, and the manufacturer's rating tables to size the components. And on any drive that moves a load a person could be hurt by, guarding and isolation are matters for the equipment's own documentation rather than for a calculator.

Reading the ratio the right way round

A recurring confusion: a ratio greater than one is a reduction — slower output, more torque. A ratio below one is an overdrive — faster output, less torque. The calculator reports 3 for the 20T-into-60T case and 0.5 for 40T-into-20T, and calling the second one "a 2:1 ratio" is where drives get specified backwards.

Stating it as "3:1 reduction" or "2:1 overdrive" removes the ambiguity, and it is worth being pedantic about on a drawing.

Belt length and centre distance

The belt length figure — 1,759.2 mm for the worked example — uses the standard open-belt approximation, and stock belts come in fixed lengths. In practice you pick the nearest stock size and adjust the centre distance to suit, which is why drives have adjustable motor mounts.

Allow take-up in both directions: enough travel to fit the belt slack and enough to tension it, plus more as the belt stretches in service. A mount with no adjustment left is a mount that needs a new belt length rather than a new belt.

Idlers change one thing and not another

An idler pulley alters wrap angle, belt path and tension — all useful — but it does not change the speed ratio, which is set by the driver and driven pulleys alone. An idler on the slack side increases wrap on the small pulley, which is generally where a friction drive runs out of grip first.

On a gear train the equivalent is an idler gear, which reverses direction and does not affect the overall ratio between the first and last gear. Both are common sources of confusion when someone counts every wheel in the train.