KHK Free Gear Calculator: How to Use It

The KHK free gear calculator is a web-based tool from KOHARA GEAR INDUSTRY (KHK) that computes gear dimensions such as module, pitch diameter, center distance, and tooth depth for standard spur and helical gears. You enter basic parameters like module, number of teeth, and pressure angle, and the calculator returns the corresponding gear geometry in both metric and inch units. This article explains what the calculator does, how to use it correctly, and where its results are reliable.

Formula

The KHK gear calculator uses standard ISO and JIS gear formulas. For a spur gear with module m (mm) and number of teeth z, the pitch diameter is:

d = m × z

Where:

• d = pitch diameter (mm)
• m = module (mm per tooth)
• z = number of teeth (dimensionless)

The addendum (height of tooth above pitch circle) is ha = m, the dedendum (depth below pitch circle) is hf = 1.25 × m for standard full-depth teeth, and the total tooth depth is h = 2.25 × m. For a pair of identical gears, the center distance is simply a = d (or a = (d1 + d2)/2 for different tooth counts).

Worked Example

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

1. Pitch diameter: d = 2 × 20 = 40.00 mm
2. Addendum: ha = 2 × 1.0 = 2.00 mm
3. Dedendum: hf = 2 × 1.25 = 2.50 mm
4. Tooth depth: h = 2 × 2.25 = 4.50 mm
5. Center distance (for a single gear, half of pitch diameter): a = (2 × 20) / 2 = 20.00 mm

These match the calculator’s outputs exactly.

What the KHK Calculator Actually Computes

The KHK online gear calculator (available on KHK’s website under “Gear Technical Reference� or “Gear Calculator�) focuses on standard gear geometry. It does not simulate stress, wear, or backlash. The tool is intended for preliminary design – you enter the module, tooth count, and pressure angle, and it gives you the basic dimensions needed to sketch or order a gear. It also includes a simple center-distance calculator for two-gear pairs, which is useful for determining the required shaft spacing.

Important: the calculator assumes standard full-depth teeth with a 20° pressure angle (or 14.5° if you select it). If you are using profile-shifted gears (also called “modified� or “X-gears�), the formulas change, and the basic calculator will not give correct results.

How to Choose the Right Inputs

To get useful results from the KHK calculator, you need to know three things:

• Module (m) – the metric gear size. Common modules are 0.5, 0.8, 1, 1.5, 2, 2.5, 3, 4, 5 mm. Larger modules mean larger teeth and higher load capacity.
• Number of teeth (z) – the actual tooth count on the gear. Minimum is usually 12–17 teeth for 20° PA to avoid undercutting.
• Pressure angle (α) – typically 20° for modern gears, 14.5° for older or fine-pitch gears.

If you are designing a gear pair, you also need the center distance or the tooth count of the second gear. The calculator can work backward: if you know the center distance and module, you can find the total tooth count.

Common Mistakes and Misconceptions

One frequent error is confusing module with diametral pitch (DP). Module is metric (mm per tooth), while DP is imperial (teeth per inch). They are not interchangeable. The KHK calculator uses module – if you have a DP value, convert it first: m = 25.4 / DP.

Another mistake is using the outside diameter (tip diameter) instead of pitch diameter. The calculator outputs pitch diameter, which is the theoretical circle where teeth mesh. The outside diameter is da = d + 2m (for standard gears). If you measure a gear’s outside diameter and divide by tooth count, you get a value slightly larger than the module – a common source of errors.

Also, the calculator does not account for backlash. Backlash is the intentional gap between meshing teeth, and it must be added separately in the design. KHK provides a separate backlash table in their catalog, not in the basic calculator.

Limits of the KHK Calculator

The KHK free tool is not a full gear design package. It does not compute:

• Tooth bending strength or surface durability (AGMA or ISO ratings)
• Contact ratio or interference checks
• Helical gear lead and helix angle effects (the calculator is mainly for spur gears)
• Profile shift values or backlash specifications

For those, you would need dedicated gear design software or KHK’s standard gear catalogs, which list pre-calculated ratings. The calculator is best used for quick dimension checks, educational purposes, or initial sizing before a more detailed analysis.

Alternatives and When to Use Them

If you need more than basic geometry, consider these alternatives:

• KHK Standard Gear Catalog – free PDF with pre-calculated dimensions for thousands of gears, including strength ratings.
• MITCalc or GearTrax – commercial software with full stress analysis and 3D modeling.
• Online calculators like this one – simple, no installation, but limited to geometry.
• Spreadsheet formulas – you can replicate the KHK formulas in Excel for custom designs.

For a hobbyist making a one-off gear, the KHK calculator is usually enough. For production machinery, you should verify with a professional design.

Frequently Asked Questions

Q: Is the KHK gear calculator free?
Yes, KHK offers its online gear calculator free of charge on its website. You do not need to register or download software. It is a simple web form that returns results instantly.

Q: What units does the KHK calculator use?
It uses metric units (millimeters for dimensions, degrees for angles). The module is in millimeters. If you need inches, you must convert manually (1 inch = 25.4 mm).

Q: Can I use it for helical gears?
The basic KHK calculator is primarily for spur gears. For helical gears, you need the normal module, helix angle, and additional formulas. KHK has a separate helical gear calculator, but it is less commonly used.

Q: Does it account for backlash?
No. The calculator gives ideal geometry. Backlash must be added by specifying a slightly larger center distance or using profile shift. KHK provides backlash tables in their catalog.

Q: What is the minimum number of teeth to avoid undercutting?
For a 20° pressure angle standard gear, the minimum is 17 teeth. Below that, undercutting weakens the tooth. For 14.5° PA, the minimum is 32 teeth. The KHK calculator does not warn you about this, so you must check manually.

Q: Why is my measured outside diameter different from the calculator?
Because the calculator outputs pitch diameter, not outside diameter. The outside diameter is pitch diameter plus two addenda (d + 2m). If you measured a gear, you likely measured the outside diameter, which is slightly larger.

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in module | Module (m) | mm | 2 | 0
in teeth | Number of teeth (z) | - | 20 | 1
in angle | Pressure angle (α) | deg | 20 | 0
out pitch_d | Pitch diameter (d) | mm | module * teeth | 2
out addendum | Addendum (ha) | mm | module | 2
out dedendum | Dedendum (hf) | mm | 1.25 * module | 2
out tooth_depth | Tooth depth (h) | mm | 2.25 * module | 2
out center_dist | Center distance (a) | mm | (module * teeth) / 2 | 2