KHK Gear Calculator: How to Use It

The KHK gear calculator is a free online tool from Kohara Gear Industry (KHK) that computes basic gear dimensions — such as reference diameter, outside diameter, center distance, and gear ratio — from a few input values like module, number of teeth, and pressure angle. You enter the gear specs, and it returns the standard metric gear calculations based on ISO/JIS formulas, which is useful for quick design checks and educational reference. Below, we explain what the calculator does, how to use it, and what its limitations are.

Formula

The calculator uses the standard metric gear formulas defined in ISO 53 and JIS B 1701. For a spur gear with module m (mm), number of teeth z, pressure angle α (degrees), and profile shift coefficient x:

• Reference diameter (pitch diameter): d = m × z
• Outside diameter (tip diameter): d_a = m × (z + 2 + 2x)
• Root diameter: d_f = m × (z − 2.5 + 2x)
• Base circle diameter: d_b = m × z × cos(α)

All dimensions are in millimeters. The module is the ratio of the reference diameter to the number of teeth (m = d / z). The pressure angle is the angle between the line of action and the common tangent of the base circles; for standard gears it is 20° (14.5° is also used in older inch-based systems).

Worked Example

Using the default values from the calculator above (module = 2 mm, teeth = 20, pressure angle = 20°, profile shift = 0):

1. Reference diameter: d = 2 × 20 = 40.00 mm
2. Outside diameter: d_a = 2 × (20 + 2 + 0) = 44.00 mm
3. Root diameter: d_f = 2 × (20 − 2.5 + 0) = 35.00 mm
4. Base circle diameter: d_b = 2 × 20 × cos(20°) = 40 × 0.93969 = 37.59 mm

These match the calculator’s outputs: 40.00, 44.00, 35.00, and 37.59 mm.

How to Use the KHK Gear Calculator

KHK’s online calculator (found on their website under “Gear Technical Reference�) lets you pick a gear type (spur, helical, bevel, worm, etc.) and then enter the relevant parameters. For a standard spur gear, the typical inputs are:

• Module (m) – the metric size of the teeth, in mm (common values: 0.5, 1, 1.5, 2, 3, 4, 5)
• Number of teeth (z) – integer between 6 and several hundred
• Pressure angle (α) – usually 20° for standard metric gears
• Profile shift coefficient (x) – 0 for standard gears, positive or negative for modified gears

The calculator then outputs the reference diameter, outside diameter, root diameter, base circle diameter, and sometimes the center distance when you also input the mating gear’s teeth. For a gear pair, the center distance is (d1 + d2) / 2 for standard (unshifted) gears.

What the Results Mean

The reference diameter is the theoretical circle where two gears mesh without backlash; it is used to calculate gear ratio and center distance. The outside diameter is the physical tip circle, which matters for housing clearance and interference. The root diameter is the bottom of the tooth spaces, important for strength and for avoiding undercut. The base circle diameter is used to construct the involute tooth profile; the involute curve is generated by unwinding a string from this circle. In practice, you use these dimensions to check whether a gear will fit in a given envelope, to compute the speed ratio (z2/z1), and to ensure proper backlash.

Common Mistakes and Misconceptions

• Confusing module with diametral pitch: Module (mm) is the inverse of diametral pitch (teeth per inch). A gear with module 2 has teeth that are 2 mm in size; a gear with diametral pitch 2 has teeth that are 12.7 mm in size (25.4 / 2). The calculator uses metric module only.
• Using the wrong pressure angle: Most metric gears are 20°, but some older or special gears use 14.5° or 25°. Using the wrong angle changes the base circle and the shape of the tooth, but the reference diameter and outside diameter do not depend on the pressure angle.
• Forgetting profile shift: If a gear has a profile shift (x ≠ 0), the outside and root diameters change, but the reference diameter remains the same. The calculator includes x, so enter it correctly.
• Assuming the calculator gives the center distance for all cases: For standard gears, center distance = (d1 + d2) / 2. For shifted gears, the center distance changes, and the KHK calculator may not compute it unless you use the specific “center distanceâ€� mode.

Limitations of the KHK Calculator

The KHK calculator is a design reference, not a full engineering analysis. It does not calculate tooth strength, wear, backlash, or manufacturing tolerances. It assumes standard involute gears with a defined module and pressure angle. For non-standard gears (e.g., with modified tooth profiles, or internal gears), the formulas differ. Also, the calculator gives theoretical dimensions; actual gears have tolerances (e.g., ISO 7H or 8e) that affect the final mesh. For production, you need to consult gear data sheets or use specialized software like KISSsoft or MITCalc.

Alternatives to the KHK Calculator

If you need more advanced calculations, consider:

• MITCalc – a commercial Excel add-in with detailed strength and geometry calculations.
• KISSsoft – professional gear design software with 3D modeling and analysis.
• Online calculators – many engineering websites offer free gear calculators, but they may use different formulas or units. Always verify the formulas.
• Manual calculation – the formulas above are simple enough for a spreadsheet. For a gear pair, you also need the center distance formula.

Frequently Asked Questions

What is the module in a gear?

The module (m) is the ratio of the reference diameter to the number of teeth, expressed in millimeters. It defines the tooth size. A module 2 gear has teeth that are 2 mm in size (the reference diameter is 2 × z mm).

How do I calculate the center distance between two gears?

For two standard spur gears with teeth z1 and z2 and module m, the center distance is m × (z1 + z2) / 2. For example, a 20-tooth and a 40-tooth gear with module 2 have center distance = 2 × (20 + 40) / 2 = 60 mm.

What is the difference between reference diameter and outside diameter?

Reference diameter is the theoretical pitch circle used for calculations; outside diameter is the physical tip circle. Outside diameter is always larger than reference diameter (by 2 × module for standard gears).

Can I use the KHK calculator for helical gears?

Yes, KHK’s site has separate calculators for helical gears. For helical gears, you need to input the helix angle (β) and the normal module (m_n). The formulas are different: the reference diameter is m_n × z / cos(β).

Why does my gear have undercut?

Undercut occurs when the number of teeth is too small (typically below 17 for a 20° pressure angle, without profile shift). The KHK calculator will show the root diameter, but it does not warn about undercut. To avoid undercut, use a larger number of teeth or apply a positive profile shift (x).

Does the calculator account for backlash?

No, the KHK calculator gives nominal dimensions without backlash. Backlash is the intentional gap between meshing teeth, which is achieved by adjusting center distance or using profile shift. The calculator does not include backlash values.

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in m | Module (m) | mm | 2 | 0
in z | Number of teeth (z) | - | 20 | 0
in alpha | Pressure angle (α) | deg | 20 | 0
in x | Profile shift coefficient (x) | - | 0 | 0
out d | Reference diameter (d) | mm | m * z | 2
out da | Outside diameter (da) | mm | m * (z + 2 + 2*x) | 2
out df | Root diameter (df) | mm | m * (z - 2.5 + 2*x) | 2
out base | Base circle diameter (db) | mm | m * z * cos(alpha) | 2