Thread Calculator: Pitch, Diameter and Tap Drill Size
Enter a thread standard, size and pitch to calculate every key dimension: major diameter, pitch diameter, minor diameter, thread depth, threads per inch, lead angle, and recommended tap drill size. Covers metric ISO and Unified Imperial (UNC and UNF) threads. Results update as you type, with a step-by-step breakdown of the formulas.
Formula
Worked example
For M10 x 1.5: H = 0.866 x 1.5 = 1.299 mm. Thread depth = 5/8 x 1.299 = 0.812 mm. Pitch diameter = 10 - 0.6495 x 1.5 = 9.026 mm. Minor diameter = 10 - 1.2269 x 1.5 = 8.160 mm. Tap drill = 10 - 1.5 = 8.5 mm.
What is thread pitch and why does it matter?
Thread pitch is the distance from one thread crest to the next, measured parallel to the thread axis. It determines how much a fastener advances axially per revolution: a fine pitch moves the bolt less per turn, giving finer adjustment and better vibration resistance; a coarse pitch allows faster assembly and greater resistance to stripping in soft materials. In the metric ISO system, pitch is stated directly in millimetres (for example, M10 x 1.5 means 1.5 mm between crests). In the Unified Imperial system, the equivalent quantity is threads per inch (TPI), and pitch in inches is simply 1 divided by TPI.
Thread geometry: major, pitch and minor diameters explained
A 60-degree V-thread has three characteristic diameters. The major diameter is the largest diameter of the thread, corresponding to the crests on an external (bolt) thread or the roots on an internal (nut) thread. It matches the nominal designation (M10 has a 10 mm major diameter). The pitch diameter is the theoretical cylinder where thread thickness exactly equals the space between threads - it is the datum for thread engagement and tolerance. The minor diameter is the smallest diameter, at the roots of an external thread. All three follow from the fundamental triangle height H = (sqrt(3)/2) x pitch: pitch dia = major - 0.6495 x pitch, minor dia = major - 1.2269 x pitch, thread depth = (5/8) x H.
Tap drill selection: balancing strength and tool life
The tap drill diameter determines the percentage of thread engagement in a tapped hole. A common rule of thumb is major diameter minus pitch, which gives approximately 75% thread engagement. Research and industry practice show that 75% engagement provides about 95% of the theoretical thread strength, while full (100%) engagement barely improves pullout strength and dramatically increases the torque needed to tap the hole, raising the risk of tap breakage. For through-holes in strong materials (steel, stainless) use 75%; for blind holes in soft materials (aluminium, plastic) you may use 50-60% engagement (a slightly larger drill) to reduce tap breakage. Always verify the tap drill against a standard chart for your specific material.
Metric ISO vs. Unified Imperial: choosing the right standard
Metric ISO threads (M-series) are used almost universally in machinery, automotive, and consumer products worldwide. They are defined by nominal diameter and pitch in millimetres. The coarse series is the default for general fastening; the fine series (smaller pitch for a given diameter) is used where vibration resistance or fine adjustment is needed. Unified threads (UNC for coarse, UNF for fine, UNEF for extra fine) are the standard in North America and remain common in aerospace. UNC is preferred for rapid assembly and tapping in soft materials; UNF gives better fatigue resistance. Both use the same 60-degree flank angle and the same ISO 68 thread form, so the underlying geometry formulas are identical - only the pitch and nominal diameter values differ.
Common metric ISO coarse thread dimensions (external / bolt)
| Size | Pitch (mm) | Pitch dia (mm) | Minor dia (mm) | Tap drill (mm) |
|---|---|---|---|---|
| M3 | 0.50 | 2.675 | 2.387 | 2.50 |
| M4 | 0.70 | 3.545 | 3.141 | 3.30 |
| M5 | 0.80 | 4.480 | 4.019 | 4.20 |
| M6 | 1.00 | 5.350 | 4.773 | 5.00 |
| M8 | 1.25 | 7.188 | 6.466 | 6.75 |
| M10 | 1.50 | 9.026 | 8.160 | 8.50 |
| M12 | 1.75 | 10.863 | 9.853 | 10.25 |
| M16 | 2.00 | 14.701 | 13.546 | 14.00 |
| M20 | 2.50 | 18.376 | 16.933 | 17.50 |
| M24 | 3.00 | 22.051 | 20.319 | 21.00 |
Major diameter, pitch, pitch diameter, minor diameter and tap drill size for standard metric coarse external threads. All values in millimetres.
Frequently asked questions
What is the difference between pitch and lead?
Pitch is the distance between adjacent thread crests. Lead is the axial distance the thread advances in one full revolution. For a standard single-start thread (the vast majority of fasteners) pitch and lead are the same. For a multi-start thread - where two or more helical grooves are cut side by side - the lead equals the pitch multiplied by the number of starts. A 2-start M10 x 1.5 thread advances 3 mm per revolution instead of 1.5 mm, allowing faster assembly without changing the pitch or strength.
How do I convert between pitch (mm) and TPI?
TPI = 25.4 / pitch (mm) and pitch (mm) = 25.4 / TPI. For example, a 1.5 mm pitch equals 25.4 / 1.5 = 16.93 TPI. A 13 TPI thread has a pitch of 25.4 / 13 = 1.954 mm. This calculator shows both values automatically.
What tap drill size should I use for metric threads?
The standard approximation is tap drill diameter = major diameter minus pitch. For M10 x 1.5 that gives 10 - 1.5 = 8.5 mm, which is the drill commonly specified in tap charts. This yields about 75% thread engagement, the standard workshop target. If you are working in very soft materials and want to reduce tap breakage risk, a slightly larger drill (giving 50-60% engagement) is acceptable because the material itself contributes to pullout strength.
What is the pitch diameter and why is it important?
The pitch diameter is the imaginary cylinder where the thread thickness equals the space between threads. It is the key functional diameter because it controls how well a bolt and nut mate: if two mating threads have the same pitch diameter within their tolerance band, they will mesh correctly. Thread gauges and tolerance specifications - such as the 6g/6H system for metric threads - define allowable deviations from the theoretical pitch diameter. Major and minor diameters matter for clearance and strength; pitch diameter matters for fit and function.
Is UNC coarser than UNF for the same diameter?
Yes. "Coarse" means fewer threads per inch (larger pitch), and "fine" means more threads per inch (smaller pitch). For a 1/2-inch fastener, UNC is 1/2-13 (13 TPI, pitch = 1.954 mm) and UNF is 1/2-20 (20 TPI, pitch = 1.270 mm). UNC is faster to assemble and more forgiving in soft or dirty threads; UNF is better for precision adjustment, vibration-prone joints, and thin-walled materials.
How do I measure thread pitch without a gauge?
Place a ruler along the thread and count the number of crests over a known length, then divide the length by the crest count. For example, if you count 10 complete threads over 15 mm, pitch = 15 / 10 = 1.5 mm. For imperial threads, count crests over exactly 1 inch - that count is the TPI. A thread pitch gauge (comb gauge) is faster and more accurate for production work, but the ruler method works reliably for identification purposes.