How to use this calculator
- Choose the measured diameter. Use pitch diameter when it is known, or tip/outside diameter when measuring an existing standard full-depth gear.
- Enter the measured diameter. Enter the selected pitch or outside diameter.
- Enter the tooth count. Enter the number of teeth on the gear.
- Read the module check. Read the measured module, nearest ISO module, percent delta, diametral pitch, circular pitch, addendum and whole depth.
How it works
The module sets a gear's tooth size. It is the pitch diameter per
tooth:
m = d / z
where d is the pitch diameter and z the tooth count. The
imperial equivalent is the diametral pitch DP = 25.4 / m (1/in) — module and DP are reciprocals scaled by 25.4, so
m = 25.4 / DP. The circular pitch (arc length per tooth
along the pitch circle) is p = π · m. For standard full-depth teeth the
addendum equals the module (a = m) and the whole depth is
2.25 · m. Mating gears must share the same module (or DP) and pressure
angle. For a fuller explanation of the two pitch systems, see the
module and diametral pitch guide;
if you know module or DP but need pitch diameter, use the
pitch diameter calculator.
If you are measuring an existing spur gear, the outside tip diameter is often easier
to measure than the pitch circle. In that mode the calculator uses the standard
full-depth estimate m ≈ d_a / (z + 2), back-calculates pitch diameter
as d = m · z, then compares the measured module with the nearest
ISO 54 listed module. The delta is a measurement sanity check: a large delta usually
means the wrong diameter basis, a non-standard/profile-shifted gear, wear, or a bad
tooth count.
Once the tooth size is known, the involute gear calculator expands it into pitch, base, tip and root diameters, while the gear center distance calculator checks the mesh spacing for a mating tooth count.
Worked example
Verified against the live calculator
A gear with a 40 mm pitch diameter and z = 20 teeth has
module m = 40 / 20 = 2 mm — equivalently
DP = 25.4 / 2 ≈ 12.7 (1/in). Its circular pitch is
π · 2 ≈ 6.28 mm, the addendum is 2 mm, and the whole depth
is 2.25 × 2 = 4.5 mm. The calculator returns exactly this.
For an existing 19-tooth gear measured over the tips at
41.8 mm, the outside-diameter method gives
m ≈ 41.8 / (19 + 2) = 1.99 mm. The nearest ISO module is
2 mm, so the measurement is close enough to treat module 2 as the
likely standard tooth size before checking pressure angle and the mating gear.
Frequently asked questions
How do you calculate the gear module?
Module m = pitch diameter d ÷ number of teeth z. If you measured the outside tip diameter of a standard full-depth gear, use m ≈ tip diameter ÷ (z + 2). The calculator supports both measurement methods and compares the result with the nearest ISO module.
What is the difference between module and diametral pitch?
They are the metric and imperial measures of the same tooth size and are reciprocals scaled by 25.4: module (mm) m = 25.4 / DP, and diametral pitch (1/in) DP = 25.4 / m. So module 2 mm is about DP 12.7, and DP 10 is module 2.54 mm.
How do I measure the module of an existing gear?
Count the teeth z and measure the tip (outside) diameter. For a standard full-depth tooth the tip diameter ≈ m·(z + 2), so module m ≈ tip diameter ÷ (z + 2). Confirm against the standard module series — a 41.8 mm tip with 19 teeth gives m ≈ 1.99, i.e. module 2.
What is circular pitch?
Circular pitch p is the distance from one tooth to the next measured along the pitch circle: p = π · m. It is the arc length per tooth, whereas the module is the pitch diameter per tooth.
What are the standard module sizes?
ISO 54 lists preferred metric modules. Series 1 is the first-choice series; Series 2 is secondary when Series 1 cannot be applied. The calculator reports the nearest listed module, its series and the percent delta from your measured value.
Does this work in metric and imperial?
Yes — toggle SI/Imperial in the header to switch the diameters between mm and inches. The module is always shown in mm and the diametral pitch in 1/in, so you get both systems at once.
Method & assumptions
- Standard full-depth involute proportions (addendum = m, whole depth = 2.25 m). Stub or non-standard tooth systems differ.
- Tip/outside-diameter mode assumes a standard full-depth external spur gear. Profile shift, wear, chamfers and non-standard tooth systems move the estimate.
- Nearest ISO module is a measurement check, not proof of pressure angle, backlash, tooth quality or interchangeability.
- Module (mm) and diametral pitch (1/in) are reciprocals scaled by 25.4: m = 25.4 / DP.