Gear calculator
A module 2 pair of 18 and 36 teeth runs at a 54.000 mm centre distance (a = m·(z₁ + z₂) / 2), on pitch diameters of 36.000 and 72.000 mm; the pinion checks at 15.265 mm over 3 teeth. Enter the module or diametral pitch, the pressure angle, the helix angle and both tooth counts, with any profile shift, for the sizes, the centre distance and the span or over-pins measurement a drawing gives the tooth thickness by.
The pair is drawn in mesh with its true involute teeth, and the ISO 54 modules load from the table.
- Centre distance a
- Ratio z₂ / z₁
- Pitch Ø d₁ / d₂
- Tip Ø da₁ / da₂
- Root Ø df₁ / df₂
- Span W over 3 teeth (pinion)
- Over pins M, Ø3.462 (pinion)
- Ideal pin Ø (pinion)
- Working pressure angle αw
- Top land (pinion)
How it’s calculated
inv α = tan α − α. The increment y is 0 for an unshifted pair; with profile shift, inv αw = 2·tan α·(x₁ + x₂)/(z₁ + z₂) + inv αt and y = (z₁ + z₂)/(2 cos β)·(cos αt / cos αw − 1). Each tip is da = d + 2(1 + y − x_other)·m, the whole depth h = (2.25 + y − (x₁ + x₂))·m. Over pins: inv φ = dp/(m·z·cos α) − π/2z + inv αt + 2x·tan α/z, M = db/cos φ + dp (even z). Here: a = 54.000 mm, and the pinion spans k = 3 teeth, W = 15.265 mm.
| Module m | Series | Circular pitch p | DP (1/in) | d₁ (mm) | a (mm) |
|---|---|---|---|---|---|
| 1 | I (preferred) | 3.142 | 25.400 | 18.000 | 27.000 |
| 1.125 | II | 3.534 | 22.578 | 20.250 | 30.375 |
| 1.25 | I (preferred) | 3.927 | 20.320 | 22.500 | 33.750 |
| 1.375 | II | 4.320 | 18.473 | 24.750 | 37.125 |
| 1.5 | I (preferred) | 4.712 | 16.933 | 27.000 | 40.500 |
| 1.75 | II | 5.498 | 14.514 | 31.500 | 47.250 |
| 2 | I (preferred) | 6.283 | 12.700 | 36.000 | 54.000 |
| 2.25 | II | 7.069 | 11.289 | 40.500 | 60.750 |
| 2.5 | I (preferred) | 7.854 | 10.160 | 45.000 | 67.500 |
| 2.75 | II | 8.639 | 9.236 | 49.500 | 74.250 |
| 3 | I (preferred) | 9.425 | 8.467 | 54.000 | 81.000 |
| 3.5 | II | 10.996 | 7.257 | 63.000 | 94.500 |
| 4 | I (preferred) | 12.566 | 6.350 | 72.000 | 108.000 |
| 4.5 | II | 14.137 | 5.644 | 81.000 | 121.500 |
| 5 | I (preferred) | 15.708 | 5.080 | 90.000 | 135.000 |
| 5.5 | II | 17.279 | 4.618 | 99.000 | 148.500 |
| 6 | I (preferred) | 18.850 | 4.233 | 108.000 | 162.000 |
| 6.5 | II (avoid) | 20.420 | 3.908 | 117.000 | 175.500 |
| 7 | II | 21.991 | 3.629 | 126.000 | 189.000 |
| 8 | I (preferred) | 25.133 | 3.175 | 144.000 | 216.000 |
| 9 | II | 28.274 | 2.822 | 162.000 | 243.000 |
| 10 | I (preferred) | 31.416 | 2.540 | 180.000 | 270.000 |
| 11 | II | 34.558 | 2.309 | 198.000 | 297.000 |
| 12 | I (preferred) | 37.699 | 2.117 | 216.000 | 324.000 |
| 14 | II | 43.982 | 1.814 | 252.000 | 378.000 |
| 16 | I (preferred) | 50.265 | 1.587 | 288.000 | 432.000 |
| 18 | II | 56.549 | 1.411 | 324.000 | 486.000 |
| 20 | I (preferred) | 62.832 | 1.270 | 360.000 | 540.000 |
| 22 | II | 69.115 | 1.155 | 396.000 | 594.000 |
| 25 | I (preferred) | 78.540 | 1.016 | 450.000 | 675.000 |
| 28 | II | 87.965 | 0.907 | 504.000 | 756.000 |
| 32 | I (preferred) | 100.531 | 0.794 | 576.000 | 864.000 |
| 36 | II | 113.097 | 0.706 | 648.000 | 972.000 |
| 40 | I (preferred) | 125.664 | 0.635 | 720.000 | 1080.000 |
| 45 | II | 141.372 | 0.564 | 810.000 | 1215.000 |
| 50 | I (preferred) | 157.080 | 0.508 | 900.000 | 1350.000 |
Span or over pins: how is a gear tooth checked?
A gear drawing gives the tooth thickness as a measurement a machinist can take on the part. The span (base tangent length) W is read with a disc micrometer across k teeth: its anvils sit on two opposite flanks along a tangent to the base circle, so the reading is the same wherever it is taken and needs no centres. Over pins, two pins of a set size sit in opposite spaces and a micrometer reads over them; on an odd tooth count the spaces are not opposite and the formula allows for it. A helical gear is measured over balls. Both depend on the profile shift, which is why a drawing that shifts the teeth gives x with them.