Worked example
Module 2 with 20 and 50 teeth: pitch diameters 2 × 20 = 40 mm and 2 × 50 = 100 mm; outside diameters 40 + 4 = 44 mm and 100 + 4 = 104 mm; centre distance (40 + 100) / 2 = 70 mm; ratio 50 / 20 = 2.5. The circular pitch is π × 2 = 6.283 mm. The gear blank for the pinion is turned to the outside diameter, 44 mm.
What the terms mean
- Module is the pitch diameter per tooth in millimetres; a larger module means bigger teeth. Two gears must have the same module to mesh.
- Pitch diameter is the diameter of the pitch circle, where the two gears roll on each other.
- Centre distance is the distance between the two shafts – the sum of the two pitch radii.
- Ratio is the factor by which the speed falls from pinion to gear; torque rises by the same factor (see the torque calculator).
Frequently asked questions
How do I calculate the pitch diameter of a spur gear?
d = m × z, the module times the number of teeth. Module 2 with 20 teeth gives 40 mm.
How do I calculate the outside diameter?
da = d + 2 × m for a standard gear with no profile shift: 40 + 4 = 44 mm.
How do I calculate the centre distance of two gears?
a = m × (z1 + z2) / 2. Module 2 with 20 and 50 teeth gives 70 mm.
What is the module of a gear?
The pitch diameter per tooth in millimetres. Gears must have the same module to mesh; for imperial gears, module = 25.4 / diametral pitch.
More free machinist calculators
- Inch to mm – Convert inches to millimetres and back, fractions like 1 3/8 included. Exact factor 25.4, with a chart of every 1/64 inch.
- RPM and feed – Calculate spindle RPM from surface speed and diameter, surface speed from RPM, and feed rate from chip load – metric and imperial, with formulas.
- Taper – Taper ratio, half angle and taper per foot from the large and small diameter and the length, or the small diameter from the angle.
- Bolt circle – X and Y coordinates of evenly spaced holes on a bolt circle, with the hole spacing, start angle and centre offset. Copy the table into your program.
- Sine bar – Gauge block height for a sine bar angle, or the angle from a known stack, for 5 in, 10 in, 100 mm, 200 mm or any other bar length.
- Metal removal rate – Metal removal rate in cm³/min or in³/min from depth, width and feed – milling and turning, metric and imperial, with the formulas.
- Drill point depth – Length of a drill's point cone from diameter and point angle, and the total depth needed for a full-diameter hole to depth.
- Right triangle – Hypotenuse and angles from two legs, or the legs from the hypotenuse and an angle – for chamfers, dovetails, tapers and hole positions.
- Machining time – Cutting time from length, feed and spindle speed – turning with feed per revolution, milling with feed rate and number of passes.
- Decimal to fraction – Turn a decimal inch or a millimetre value into the nearest fraction – 8ths to 128ths – with the error in millimetres.
- Degrees to DMS – Convert decimal degrees to degrees, minutes and seconds and back, with the angle in radians.
- SFM to m/min – Convert surface feet per minute to metres per minute and back, and inches per minute to mm per minute, with the exact factors.
- TPI to pitch – Convert a thread pitch in millimetres to threads per inch (TPI) and back, for matching metric and inch threads.
- Cpk calculator – Paste measurements from Excel, enter USL and LSL and get Cp, Cpk, Pp and Ppk. Says plainly when 25 values are too few for an index.
- Tolerance stack-up – Add up the tolerances of a chain of parts: closing gap, worst case and statistical RSS for up to eight dimensions. Free, in your browser.
- Fit clearance – Enter hole and shaft limits and get minimum and maximum clearance and the kind of fit – clearance, transition or interference.
- Chip thinning – Feed per tooth to program when the radial width of cut is below half the cutter diameter, so the real chip thickness stays right.
- Ball-nose stepover – Scallop height left by a ball-nose cutter from the stepover, or the stepover for a wanted scallop height, on a flat surface.
- Surface finish – Theoretical Rt and estimated Ra of a turned surface from the feed per revolution and the tool nose radius.
- Torque and power – Torque from power and speed in newton-metres or pound-feet, and power from torque and speed. The formulas with worked examples.
Making parts for a customer who wants paperwork?
Automotive and aerospace customers ask for proof that the parts match the drawing. See first article inspection (FAI), PPAP explained and the true position calculator.