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Gear Spacing Calculator

Exactly how far apart two gears must sit, which holes that lands on, and what to do when they cannot go on the same rail.

Inputs

VEX spur gears split into two families, shown in the list. A pair only mounts on standard holes if both come from the same one.

Pick a partner. Mixing family A with family B lands the center distance on a quarter inch, which no hole reaches.

Results

Center distance

—in

Holes apart, in a straight line

—

First gear pitch diameter

—in

Second gear pitch diameter

—in

Lands on the hole grid?

—

See them mesh

See them mesh
0°

Both gears drawn at their real pitch diameters, the distance between them at the real center distance, and the hole grid behind at the real half inch spacing. Turn the driving gear and watch the other one go the opposite way, slower or faster depending on the tooth counts.

How this is calculated

Gears mesh properly at exactly one distance apart. Too close and they bind; too far and they skip teeth under load. That distance is set by the two pitch diameters:

pitch diameter = teeth ÷ 24 center distance = (pitch diameter A + pitch diameter B) ÷ 2 = (teeth A + teeth B) ÷ 48

The 24 is VEX's diametral pitch, the number of teeth per inch of pitch diameter. It is the same for all VEX spur gears, which is why any two of them will mesh with each other.

Why standard gears always work out

VEX structure has holes every 0.5". For two gears to mount on the same rail, the center distance must be a whole number of hole spacings.

With VEX's four spur gears this is automatic. 12, 36, 60 and 84 are all multiples of 12 that leave the same remainder when divided by 24, so any pair of them sums to a multiple of 24, and dividing by 48 always gives a clean multiple of 0.5. Every standard VEX spur pair lands exactly on the grid. You do not have to check. It is only when you mix in high-strength gears, non-VEX gears or unusual tooth counts that the arithmetic stops being kind.

When they cannot share a rail

Sometimes the two shafts have to sit on different pieces of structure, so the gap between them is a diagonal rather than a straight run of holes. The distance between any two holes offset a holes across andb holes up is:

distance = 0.5 × √(a² + b²)

Very few of those diagonals land on a useful gear distance, so when the required spacing is not a straight run this calculator searches the combinations and shows the closest fits, with the error on each. Anything off by more than about 0.01" will mesh badly. Treat a near miss as a reason to move the mounting, not something to force together.

Sources & assumptions

Tooth counts are VEX's published spur gear sizes and the 0.5" hole spacing is a verified VEX standard. The 24 diametral pitch figure isderived, not published: it is the value consistent with both VEX's gear sizes and the hole grid, and it reproduces the center distances teams measure in practice.

Assumes standard external spur gears at their nominal pitch diameter, with no deliberate slop. Real builds tolerate a few thousandths of an inch; they do not tolerate a sixteenth.

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                                Comes after

                                Gear Ratio Calculatorfills in your gear sizes hereGear Train Calculatorfills in your gear sizes hereGear Ratio Solvergives you your gear sizesMechanical AdvantageLift Speed & Gear Ratio

                                You are here

                                Gear Spacing Calculator

                                Where your answer goes

                                Gear Ratio Calculatorsee what that gear pair does to your speed and torquebrings your gear sizes with itChain Length Calculatorif the holes do not line up, see if chain can span that gapbrings your center distance with itGear Train Calculatorsee what a whole train of stages like this costs in friction and playbrings your gear sizes with itSpacer Stack Calculatorwork out the spacers that keep those gears lined up on their shafts

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