Thread Pitch Calculator
Find the pitch diameter and minor diameter of an ISO metric screw thread from its major diameter and pitch.
🔧 What is Thread Pitch?
Thread pitch is the axial distance between one thread crest and the next along an ISO metric screw thread, and it fully determines two other critical thread dimensions once the major diameter is known: pitch diameter (d2), the reference diameter where thread flank widths are equal, and minor diameter (d3), the diameter at the thread's root. The ISO 724 standard defines exact formulas for both from major diameter D and pitch P.
Mechanical engineers, machinists, and fastener designers use these formulas to verify thread dimensions against manufacturing drawings, select the correct thread gauge for inspection, and cross-reference between metric and imperial (TPI-based) fastener systems. Every standard metric bolt, screw, and threaded hole ultimately traces back to these two formulas for its precise pitch and minor diameters.
A common point of confusion is mixing up the external (bolt) thread's minor diameter with the internal (nut) thread's basic minor diameter, they use different coefficients (1.226869 versus 1.082532) because a bolt's thread root is cut differently from a nut's thread crest, this calculator specifically computes the external thread's minor diameter, the dimension most often needed when checking a bolt or screw.
This calculator computes pitch diameter and minor diameter directly from your entered major diameter and pitch, verified against standard ISO metric thread tables, and shows the equivalent threads-per-inch value alongside a labeled thread profile diagram.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — M10 x 1.5 (Standard Coarse Pitch)
D = 10 mm, P = 1.5 mm
Example 2 — M6 x 1.0 (Standard Coarse Pitch)
D = 6 mm, P = 1.0 mm
Example 3 — M20 x 2.5 (Standard Coarse Pitch)
D = 20 mm, P = 2.5 mm
❓ Frequently Asked Questions
🔗 Related Calculators
What is thread pitch?
Thread pitch is the axial distance between one thread crest and the next, measured in millimeters for ISO metric threads. It appears directly in a thread's designation, for example M10x1.5 has a 1.5 mm pitch, and determines how far a fastener advances per full turn.
What is the formula for pitch diameter?
d2 = D - 0.649519 x P, where D is the major (nominal) diameter and P is the pitch. Pitch diameter is the diameter at which the thread's groove width equals the thread's ridge width, a key reference dimension for thread gauging.
What is the formula for minor diameter?
d3 = D - 1.226869 x P for the external (bolt) thread's minor diameter, the diameter at the root of the thread. The internal (nut) thread's basic minor diameter D1 uses a slightly different coefficient, D1 = D - 1.082532 x P.
How do I convert metric pitch to threads per inch (TPI)?
TPI = 25.4 / P, where P is the pitch in millimeters and 25.4 is the number of millimeters in one inch. For example, a 1.5 mm pitch converts to 25.4/1.5 = 16.93 TPI, useful for comparing against imperial (UN/UNC/UNF) thread charts.
What does the M10x1.5 designation mean?
M indicates an ISO metric thread, 10 is the major (nominal) diameter in millimeters, and 1.5 is the pitch in millimeters. This is the standard (coarse pitch is often left unstated, e.g. plain M10 usually implies the standard 1.5 mm coarse pitch, while M10x1.25 explicitly specifies a finer pitch).
What is the difference between coarse and fine thread pitch?
For a given major diameter, coarse pitch (larger P) assembles faster, is more tolerant of dirt, damage, and cross-threading, and is the default for general use. Fine pitch (smaller P) gives a larger minor diameter for the same major diameter (stronger in tension for brittle materials), finer adjustment, and better resistance to vibration loosening, common in precision and automotive applications.
Why does pitch diameter matter for thread fit?
Pitch diameter is the critical dimension thread gauges and tolerance classes are built around, since it is where the male and female thread flanks actually make contact. Two threads with the same major diameter but different actual pitch diameters (within tolerance) will have different fit tightness.
Are these formulas exact or approximations?
These are the exact ISO 724 formulas for a standard 60-degree ISO metric thread profile with a nominal (theoretical sharp-V) geometry. Real manufactured threads have additional small root/crest truncations and tolerance allowances defined in ISO 965, but the ISO 724 basic dimensions calculated here match published standard thread tables to full precision.
Can this calculator be used for UN/UNC/UNF imperial threads?
The underlying 60-degree thread geometry is the same, so the pitch and minor diameter formulas apply once the pitch is expressed in the same units as the diameter. For imperial threads specified in TPI, first convert to pitch in inches (P = 1/TPI) or convert your diameter to millimeters and use TPI = 25.4/P as shown here.
Why is minor diameter smaller than pitch diameter, which is smaller than major diameter?
The three diameters mark different points across a thread's V-shaped profile: major diameter is measured at the crest (thread peak), pitch diameter at the midpoint where flank widths are equal, and minor diameter at the root (thread valley). Since the thread profile tapers inward from crest to root, each successive diameter is necessarily smaller.