How to use this calculator
- Choose pitch basis. Enter module, diametral pitch or circular pitch.
- Enter tooth count. Enter the gear tooth count for pitch, outside and root diameters.
- Set coefficients if needed. Use 1.0 addendum and 1.25 dedendum for standard full-depth external teeth, or enter your tooth-system coefficients.
- Read tooth depth. Read addendum, dedendum, whole depth, clearance, outside diameter and root diameter.
How it works
A standard full-depth external spur gear uses the module m as
the base tooth-size scale:
addendum a = m dedendum b = 1.25m whole depth h_t = a + b = 2.25m
Diametral pitch converts to module with m = 25.4 / DP; circular
pitch converts with m = p / pi.
Once module and tooth count are known, the reference diameters follow directly:
d = m x z, d_a = d + 2a, and
d_f = d - 2b. Root clearance for a standard mating addendum is
c = b - a, which is 0.25m for the standard full-depth
coefficients.
For tooth thickness and undercut, use the gear tooth calculator. For pitch system conversion use the gear pitch calculator, and for base-circle geometry use the base circle diameter calculator. For mesh overlap, use the gear contact ratio calculator.
Worked example
Verified against the live calculator
A 20-tooth module 2 mm spur gear has addendum
2 mm, dedendum 2.5 mm, whole depth
4.5 mm and clearance 0.5 mm. Its pitch diameter is
40 mm, outside diameter is 44 mm and root diameter is
35 mm.
Frequently asked questions
How do you calculate gear addendum and dedendum?
For a standard full-depth external spur gear, addendum is a = m and dedendum is b = 1.25m, where m is module. In diametral pitch, m = 25.4/DP, so addendum is 25.4/DP in mm or 1/DP in inches.
What is gear whole depth?
Whole depth is the radial tooth depth from tip to root: h_t = addendum + dedendum. For a standard full-depth spur gear it is 2.25m.
What is the difference between working depth and whole depth?
Working depth is the part of the tooth depth that actually overlaps with the mating gear. With equal standard addenda, h_w = 2m. Whole depth includes root clearance, so h_t = 2.25m for standard full-depth teeth.
How do I calculate outside diameter and root diameter?
Pitch diameter is d = m x z. Outside diameter is d_a = d + 2a, and root diameter is d_f = d - 2b, where a is addendum, b is dedendum and z is tooth count.
Does pressure angle change addendum and dedendum?
Not for this standard tooth-proportion screen. Pressure angle changes base-circle geometry, contact ratio and tooth loading, but standard full-depth addendum and dedendum are based on module or diametral pitch.
Does this calculate backlash or gear strength?
No. This page calculates tooth-depth proportions and reference diameters. Backlash, tolerances, root fillets, contact ratio, bending/contact stress and manufacturing drawings need separate checks.
Method & assumptions
- Standard full-depth external spur gear proportions default to
a = mandb = 1.25m. - Custom addendum and dedendum coefficients are simple radial multipliers, not a full cutter or profile-shift model.
- Internal gears, stub teeth, profile shift, backlash, root fillets, contact ratio, strength rating and manufacturing tolerances are outside this screen.