Gear Calculator

Calculate your gear, see its drawing and 3D model

Enter the module and the number of teeth; pitch, tip and root diameters, centre distance and much more are calculated instantly with standard formulas. You can send the result together with its drawing in a single click.

Spur Gear Calculation

Calculates the reference, tip and root diameters, the centre distance and the contact ratio of a parallel-axis spur gear pair.

Modulem

The basic size of the tooth (pitch ÷ π).

Pinion teethz₁

Wheel teethz₂

ISO 21771 · DIN 3960 · ISO 53

Results

Gear dimensions

Quantity	Pinion	Wheel
Number of teethz	20	40
Reference diameterdd = m · z	40mm	80mm
Tip diameterdₐdₐ = d + 2m(1 + x)	44mm	84mm
Root diameterd_fd_f = d − 2m(1 + c* − x)	35mm	75mm
Base diameterd_bd_b = d · cos α	37.588mm	75.175mm
Tooth depthhh = (dₐ − d_f) / 2	4.5mm	4.5mm
Tooth thickness (at reference circle)sₙsₙ = m(π/2 + 2x · tan α)	3.142mm	3.142mm
Profile shiftx	0	0
Bore (drawing)	11mm	23mm
Approximate mass (steel)Profile area × b × 7.85 g/cm³	0.178kg	0.717kg

Gear pair

Quantity	Value
Centre distanceaa = m(z₁ + z₂) / 2	60mm
Gear ratioii = z₂ / z₁	2
Face widthbb = 10 · m	20mm
Pitchpp = π · m	6.283mm
Transverse contact ratioε_αε_α = (√(rₐ₁² − r_b₁²) + √(rₐ₂² − r_b₂²) − a sin α_w) / (π m cos α)	1.635

The drawing and the 3D model are previews generated automatically from the calculated values; they do not replace a manufacturing drawing. Exact dimensions and tolerances are set through technical approval.