Gear Ratio Calculator

How to use this calculator

1. Driven over driving, not the reverseThe driven gear is the output. Getting the order backwards inverts the ratio and turns a reduction into an overdrive.
2. Use drivetrain mode for a vehicleMultiply the gearbox ratio for the gear you are in by the final drive. Top gear is often an overdrive below 1.0, which is why the mode defaults that way.
3. Add rpm and torque to see the tradeThe two move in opposite directions by exactly the ratio, which is the whole point of gearing.
4. Add a tyre size for road speedRolling circumference converts wheel rpm into miles per hour, which is what tells you whether a gearing change is sensible.

Gears trade speed for torque, exactly

A gear pair does one thing: it exchanges rotational speed for torque, in exact proportion. Nothing is created, and apart from friction nothing is lost.

A ratio above 1 is a reduction. The output turns slower than the input and delivers proportionally more torque. A 3:1 reduction turns at a third of the speed with three times the torque.

A ratio below 1 is an overdrive. The output turns faster and delivers less torque. Top gear in most cars is an overdrive, typically around 0.8, which lets the engine sit at lower revs on the motorway.

A ratio of exactly 1 is direct drive, historically fourth gear in a four-speed box, where the input and output shafts are effectively locked together.

Power passes through unchanged. Since power is torque multiplied by angular speed, and gearing multiplies one while dividing the other by the same factor, the product is constant. That is why gearing cannot make an engine more powerful — it can only put the power where it is useful.

What gearing achieves is keeping the engine in its useful range. An internal combustion engine produces useful torque over a narrow band of revs, and a gearbox lets that band cover a wide range of road speeds. Electric motors produce full torque from zero, which is exactly why most electric cars need only a single reduction gear.

For a drivetrain, the ratios multiply. A gearbox at 3.5:1 through a final drive at 4.1:1 gives an overall 14.35:1 — first gear on a typical car. Top gear at 0.8 through the same final drive gives 2.8:1.

Idler gears between the driving and driven gear reverse the direction of rotation but do not change the ratio, which is why only the first and last gear in a simple train matter to the arithmetic.

Worked example: 12 teeth driving 36

Ratio: 36 ÷ 12 = 3.0, usually written 3:1.

That is a reduction. The output turns three times slower than the input and delivers three times the torque.

At an input of 3,000 rpm, the output turns at 3,000 ÷ 3 = 1,000 rpm.

With 200 N·m going in, 600 N·m comes out.

Check the power. Input: 200 × (2π × 3000 ÷ 60) = 200 × 314.16 = 62,832 W. Output: 600 × (2π × 1000 ÷ 60) = 600 × 104.72 = 62,832 W. Identical, as it must be — the gears traded the two components and left the product alone.

Now a drivetrain. Take a top gear of 0.8 through a final drive of 3.5, giving an overall ratio of 0.8 × 3.5 = 2.8:1.

At 3,000 engine rpm the wheels turn at 3,000 ÷ 2.8 = 1,071 rpm.

On a 205/55R16 tyre, the sidewall is 205 × 0.55 = 112.75 mm and the overall diameter is 406.4 + 225.5 = 631.9 mm, giving a rolling circumference of 1.985 m.

Road speed: 1,071 × 1.985 × 60 ÷ 1609.344 = 79.3 mph.

So this drivetrain does about 79 mph at 3,000 rpm in top, or 26.4 mph per 1,000 rpm — a figure worth knowing for any car, because it tells you immediately whether the gearing suits your driving.

Note what happens if you fit a taller tyre. A 225/45R17 has a diameter of 634.3 mm, 0.4% larger, so the same 3,000 rpm gives 79.6 mph. Small here, but a genuinely oversized tyre raises the effective gearing and dulls acceleration.

Typical ratios

The electric car row explains a genuine design difference. An electric motor produces peak torque from zero rpm and revs to perhaps 15,000, so a single fixed reduction covers the whole speed range. A combustion engine produces useful torque over maybe 3,000 rpm of a 6,000 rpm range, which is why it needs six or more ratios to do the same job.

Where gearing choices actually matter

Changing gearing is one of the few modifications that genuinely changes how a vehicle behaves, and the trade is always the same: acceleration against top speed and economy.

A numerically higher final drive — say 4.1 instead of 3.5 — multiplies torque more, so acceleration improves. But the engine revs higher at any given road speed, which costs fuel economy and raises noise. Lower gearing does the reverse.

Tyre size changes gearing without touching a gear. A taller tyre effectively lowers the numerical ratio, reducing rpm at a given speed and blunting acceleration, while a shorter one does the opposite. This is why fitting oversized wheels for appearance has real mechanical consequences, and why the speedometer reads wrong afterwards.

On bicycles the same arithmetic drives gear inches — the chainring divided by the sprocket, multiplied by wheel diameter. A 52-tooth chainring on a 13-tooth sprocket is a 4:1 ratio, giving a high gear for descending; a 34 on a 32 is roughly 1.06:1 for climbing.

For machinery, reduction gearboxes exist because electric motors are efficient at high speed and low torque, while most useful work needs the reverse. A winch, a conveyor or a mixer will use a worm or planetary reduction of anything from 10:1 to 100:1.

Worm gears deserve a mention because they have a property others lack: they can be self-locking, meaning the output cannot drive the input backwards. That makes them the standard choice for hoists and gate mechanisms where a load must not run away if power fails.

Efficiency varies by type. Spur and helical gears run at 97% to 99% per stage. Worm gears are considerably worse, sometimes 50% to 90% depending on ratio, and the losses appear as heat. A multi-stage train multiplies the losses, so a three-stage reduction at 97% per stage delivers about 91% overall.

That is why the calculated output torque is an upper bound rather than what you will measure.

Assumptions and limitations

• Ignores friction — real drivetrains lose a few percent per stage, and worm gears far more
• Assumes no tyre slip and a nominal rolling diameter, which a loaded tyre does not have
• Handles a single gear pair or a gearbox-plus-final-drive, not a full multi-stage train
• Does not model torque converters, CVTs or clutch slip
• Road speed uses nominal tyre marking geometry rather than measured circumference
• Does not check whether a gear pair is physically compatible in module or pitch
• Output torque is an upper bound rather than a measured figure

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