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Enter the module (or diametral pitch), tooth counts and, optionally, input power and speed. The page returns the dimensions to make or check each gear, the center distance to bore the housing and what comes out of the reducer: speed, torque and direction. Use it to replace a broken gear, lay out a simple reducer or understand a gearmotor nameplate.
Pre-sizing and estimating tool: results do not replace design, calculations or reports signed by a licensed professional, nor verification against the applicable codes and standards.
To scale: dashed pitch circle, tip (outside) and root circles, with the center distance dimensioned.
How to read: each gear’s dashed line is its pitch circle; the two touch at one point, where motion is transmitted. Tooth tips sit on the tip circle (dₐ, the blank diameter) and the bottom of the spaces on the root circle (d_f). Dimension "a" is the center distance between shafts, which sets the housing bores.
Bars: torque on each shaft (left axis). Line: speed (right axis).
How to read: each position on the horizontal axis is one shaft of the train, from input (motor) to output, with speed and torque written below. At each reduction, speed (line) drops by the tooth ratio and torque (bars) rises by almost the same ratio, minus losses. The output shaft is the one that needs the sturdiest bearings and keys.
How to read: z = number of teeth; d = pitch diameter; dₐ = outside (tip) diameter, the one you measure; d_f = root diameter; n = shaft speed; T = shaft torque. The highlighted row is the output gear.
How to read: i = stage ratio; a = center distance; εα = contact ratio (good above 1.2); v = pitch line velocity; Fₜ = tangential tooth force.
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Pitch diameter is d = m × z, or z ÷ DP in inches. The outside diameter (what you measure) is d + 2m (or (z + 2) ÷ DP), and the root diameter is d − 2.5m. In the example, 8 DP with 18 teeth gives a 2.25 in pitch diameter and a 2.5 in outside diameter.
Measure the outside diameter and count the teeth: DP = (z + 2) ÷ OD in inches, or m = OD ÷ (z + 2) in mm. A gear with an outside diameter of 2.5 in and 18 teeth is 8 DP. If the result is an odd number, it may be metric: divide 25.4 by the DP and check against standard modules (2, 2.5, 3…). Helical gears do not follow this simple check.
It is the average of the pitch diameters: a = (z₁ + z₂) ÷ (2 × DP) for spur gears. In the example, (18 + 63) ÷ 16 = 5.06 in. With a helix, use the transverse pitch (DP × cos β), so the distance grows with the helix angle.
At a 20° pressure angle with standard teeth, 17 teeth; below that the cutter undercuts the tooth root and weakens it. At 14.5°, 32 teeth; at 25°, 12. In practice 14 teeth at 20° is accepted with slight undercut, or a profile shift is used.
For each pair, divide driven teeth by driver teeth; in a multi-stage reducer, multiply the stage ratios. In the example, 63/18 = 3.5 and 68/17 = 4, total 14: a 1,770 rpm motor gives about 126 rpm and torque rises from about 29.7 to 399 lbf·ft at 98% efficiency per stage.
In a simple train, the middle gear does not change the final ratio, which depends only on the first and last gears. It bridges the distance between shafts and changes direction: with one idler, the output turns the same way as the input.
Helical gears have slanted teeth: they engage gradually, run quieter and carry more load for the same size, but create an axial thrust the bearings must take. Spur gears are simpler to make and have no thrust. Enter the helix angle to see the diameters and forces.
Important notice: Indus Metrics tools produce estimates and pre-sizing results from the data you enter and from published engineering methods. They do not replace design, calculations or reports signed by a licensed professional engineer (PE), nor verification against the applicable codes, standards and regulations, such as OSHA rules and the ASME codes. Material and fuel properties vary: check manufacturer data or your own process analyses before deciding. By using this site you agree to the Terms of Use.
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