Gear Tooth Calculator

Calculate involute spur gear tooth thickness, addendum, dedendum, whole depth, pitch/base/tip/root diameters and undercut margin from module or DP. Metric and imperial. Free, no signup.

Inputs

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Size system

Specify gear size by metric module or imperial diametral pitch.

Module / DP (m)

Module in mm or diametral pitch in 1/in.

Pressure angle (α)

Standard pressure angle. 20° is the common modern default.

Tooth count (z)

Number of teeth on the gear.

Profile shift (x)

Addendum-modification coefficient. Positive shift increases tooth thickness and can avoid undercut.

Results

Default result

Edit inputs

Tooth thickness at pitch(s)

3.142mm

Also computed

Addendum(a)2mm

Dedendum(b)2.5mm

Whole depth(hₜ)4.5mm

Circular pitch(p)6.283mm

Base pitch(p_b)5.904mm

Pitch diameter(d)40mm

Method notes 3 notes

Standard full-depth involute reference: addendum = m, dedendum = 1.25m, whole depth = 2.25m when profile shift x = 0.
Tooth thickness at the pitch circle is s = m·(π/2 + 2x·tan α).
Minimum teeth to avoid undercut at 20° is 18 without profile shift.

Gear tooth dimensions for a standard full-depth involute spur gear start from module m and pressure angle α. Pitch diameter is d = m·z, base diameter is d_b = d·cos α, addendum is m, dedendum is 1.25m, and tooth thickness at the pitch circle is s = m·(π/2 + 2x·tan α). This calculator also flags undercut risk.

How to use this calculator

Choose module or DP. Select the gear pitch system and enter the pitch value.
Enter pressure angle. Choose the pressure angle used by the gear cutter or gear pair.
Enter tooth count. Enter the number of teeth and optional profile shift.
Read tooth geometry. Review tooth thickness, addendum, dedendum, whole depth and undercut margin.

How it works

Standard full-depth involute gear geometry starts with module and tooth count: d = m · z d_b = d · cos α For zero profile shift, addendum is m, dedendum is 1.25m and whole depth is 2.25m. Tooth thickness at the pitch circle is: s = m · (π/2 + 2x · tan α)

Worked example

Verified against the live calculator

A 20-tooth module 2 mm, 20° gear has pitch diameter 40 mm. Tooth thickness at the pitch circle is 2 × π/2 = 3.14 mm. Addendum is 2 mm, dedendum is 2.5 mm and whole depth is 4.5 mm.

Frequently asked questions

How do you calculate gear tooth thickness?

For a standard involute spur gear, tooth thickness at the pitch circle is s = m·(π/2 + 2x·tan α), where m is module, x is profile shift and α is pressure angle.

What are addendum and dedendum?

Addendum is the radial tooth height above the pitch circle. Dedendum is the radial depth below the pitch circle. For standard full-depth teeth with x = 0, addendum is m and dedendum is 1.25m.

What is whole depth?

Whole depth is addendum plus dedendum. For a standard full-depth spur gear with no profile shift, whole depth is about 2.25m.

What is undercut?

Undercut happens when the generating tool removes material near the tooth root on low-tooth-count gears. The calculator shows the tooth-count margin against the no-undercut limit for the selected pressure angle.

Is this the same as a gear DXF generator?

No. This page focuses on tooth dimensions. Use the gear generator or gear DXF generator when you need a downloadable involute profile.

Method & assumptions

External standard full-depth involute spur gear geometry.
Profile shift affects tooth thickness, addendum and dedendum, but cutter details and root fillets are not modeled.
Backlash, tolerances, contact ratio and bending/contact stress need separate checks.

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