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Thread Calculator

Construction

Calculate the pitch diameter and minor diameter of a screw thread from major diameter and threads per inch. Free tool for machinists and toolmakers.

0.054
480

Minor Diameter

0.185
Pitch Diameter
0.218

This calculator computes your Minor Diameter, Pitch Diameter from the values you enter.

Inputs
Major DiameterThreads Per Inch (TPI)
Outputs
Minor DiameterPitch Diameter

What is a Thread?

A Thread Calculator computes the key working dimensions of a screw thread — pitch diameter and minor diameter — from just its major diameter and threads per inch (TPI). Where a single-purpose pitch diameter tool stops at one dimension, this calculator gives a fuller picture of the thread's geometry, covering both the fit dimension (pitch diameter) and the root dimension (minor diameter) in a single pass.

Screw threads are defined by three key diameters: major diameter (the outer crest-to-crest measurement), pitch diameter (the mid-flank measurement that governs fit), and minor diameter (the inner root-to-root measurement that governs strength and tap sizing). This calculator uses the standard 60-degree thread form relationships to derive the latter two from the major diameter and TPI you provide.

If you specifically need only the pitch diameter and want a narrower, more focused tool, use the Pitch Diameter Calculator instead.

How to use this Thread calculator

  1. Enter the Major Diameter in inches — the nominal outside diameter of the thread, such as 0.25 in for a 1/4-inch fastener.

  2. Enter the Threads Per Inch (TPI) for the thread, such as 20 for a 1/4-20 UNC thread or 28 for a 1/4-28 UNF thread.

  3. Read the Minor Diameter in the highlighted result card — this is the root diameter of the thread, useful for tap drill selection and strength calculations.

  4. Check the Pitch Diameter shown beneath the headline result — this is the fit-governing dimension used for thread-tolerance classes.

  5. Cross-reference a tap drill chart if you're selecting a drill bit to tap this thread — practical tap drills are sized slightly larger than the theoretical minor diameter shown here to leave a workable percentage of thread engagement.

Formula & Methodology

The calculator uses the standard theoretical relationships for a 60-degree (Unified/ISO-style) thread form:

Step 1 — Thread Pitch:

> p = 1 ÷ TPI

Step 2 — Pitch Diameter:

> PD = D − 0.64952 × p

Step 3 — Minor Diameter:

> MD = D − 1.29904 × p

Where:
- p = thread pitch in inches
- D = major diameter in inches
- PD = pitch diameter in inches
- MD = minor diameter in inches
- 0.64952 and 1.29904 = standard 60-degree thread form constants (the second is exactly double the first, reflecting the full crest-to-root depth versus the half-depth crest-to-pitch-line measurement)

Worked example — 1/4-20 thread:

- p = 1 ÷ 20 = 0.05 in
- PD = 0.25 − (0.64952 × 0.05) = 0.2175 in
- MD = 0.25 − (1.29904 × 0.05) = 0.1850 in

These theoretical values align with published dimensions for a 1/4-20 UNC thread found in ASME B1.1 reference tables. If you only need the pitch diameter figure, the narrower Pitch Diameter Calculator provides the same result with a more focused single-purpose interface.

Frequently Asked Questions

The Thread Calculator computes two key dimensions of a screw thread — pitch diameter and minor diameter — from just the major diameter and threads per inch (TPI). It gives you a fuller picture of a thread's geometry than a single-dimension tool, which is useful when you need to check both the fit diameter (pitch diameter) and the root diameter (minor diameter) of a fastener or tapped hole.
Minor diameter is the smallest diameter of a screw thread, measured across the roots of an external thread or the crests of an internal thread. It matters because it determines the core strength of a bolt (the amount of solid material left after threading) and is the dimension used to size a tap drill for cutting an internal thread.
Minor diameter and pitch diameter are both measured relative to the major diameter, but by different amounts. Pitch diameter subtracts 0.64952 times the pitch from the major diameter, while minor diameter subtracts 1.29904 times the pitch — exactly double the pitch diameter's constant. This is because minor diameter measures all the way to the thread root, while pitch diameter only measures to the midpoint of the thread flank.
In a symmetric 60-degree thread form, the crest-to-pitch-line distance and the pitch-line-to-root distance are equal on each side of the thread profile. Since pitch diameter measures one such distance (doubled for both flanks, giving 0.64952), minor diameter measures two such distances (doubled for both flanks, giving 1.29904). The geometry of the 60-degree vee thread form is what produces this exact 2x relationship.
Use this Thread Calculator when you need both pitch diameter and minor diameter from the same inputs — for example, when checking a tap drill size alongside a thread-fit dimension. If you only need pitch diameter for a fit-tolerance check, the dedicated Pitch Diameter Calculator gives the same pitch diameter result with a narrower, more focused interface.
The theoretical minor diameter calculated here represents a thread with 100% thread engagement, which is difficult to tap and prone to breaking taps. In practice, tap drill charts specify a drill slightly larger than the theoretical minor diameter to produce roughly 75% thread engagement, which is strong enough for most applications and far easier to tap. Use this calculator's minor diameter as a reference point, then consult a tap drill chart for the practical drill size.
The calculator assumes a standard 60-degree thread form, which covers Unified (UN, UNC, UNF) threads common in the US and ISO metric threads used internationally. Other thread forms, such as Acme, buttress, or pipe threads, use different geometry and would require different constants than the ones used here.
The formulas used here give the theoretical sharp-vee dimensions defined by thread standards such as ASME B1.1. Real manufactured threads have flattened or rounded roots and crests rather than a perfectly sharp point, which is accounted for by small standardized allowances in official thread tables. For design and estimation, the calculator's output is accurate; for final inspection tolerances, consult the applicable thread standard.
This calculator is built around threads per inch (TPI), which is how Unified inch threads are specified. Metric threads are specified directly by pitch in millimeters. To use this calculator for a metric thread, you would need to convert the metric pitch to an equivalent TPI value (TPI = 25.4 divided by pitch in mm) before entering it.
Both dimensions decrease as TPI decreases (pitch increases), but minor diameter decreases at twice the rate of pitch diameter because its multiplying constant (1.29904) is exactly double that of pitch diameter (0.64952). This means coarse threads (low TPI) have a proportionally larger gap between major and minor diameter than fine threads (high TPI) of the same nominal size.
Knowing both dimensions together lets you fully characterize a thread's geometry in one pass — pitch diameter for fit and tolerance checks, and minor diameter for strength calculations and tap drill selection. This is especially useful when specifying a custom threaded part or verifying a non-standard thread against design requirements.
No, the values calculated here are the theoretical basic (nominal) dimensions before any class-of-fit tolerance is applied. Thread classes such as 2A, 3A, 2B, or 3B add a tolerance band around these nominal values — external threads are sized slightly below nominal and internal threads slightly above nominal to allow for assembly clearance. This calculator gives you the baseline dimension that those tolerances are applied around.
Also known as
screw thread calculatormajor minor pitch diameter calculatorunified thread dimensions calculatorthread size calculator60 degree thread calculator