A thread designation like M10×1.5 or 1/4-20 contains only two numbers, but the whole geometry of the thread is implied by them. This thread pitch calculator unpacks that: it converts between pitch and threads per inch, and derives the basic pitch diameter, the basic minor diameter, the radial depth of the thread and the helix angle from the designation you enter.
It is worth being blunt about what this page is not, because a closely related tool already exists here. Our clearance hole calculator is about holes — its headline output is the tap drill diameter for a target thread engagement, alongside close, normal and loose clearance hole sizes. This page never headlines a tap drill size and does not size holes at all. Its subject is the thread form itself: the dimensions of the helix cut into or onto the fastener. Arb Digital keeps the two separate deliberately, because they are asked by different people at different points in a job.
What This Thread Pitch Calculator Does
Enter a system, a nominal major diameter and either a pitch in millimetres or a count of threads per inch, and it returns the equivalent in the other unit, the basic pitch diameter, the basic minor diameter, the radial depth of one thread flank, the fundamental triangle height, the lead, the helix angle at the pitch diameter, and the number of threads engaged over a stated length.
Both the ISO metric and the Unified inch systems share a 60-degree symmetric thread form, so once pitch and threads per inch are related the same formulas apply to both. That is why the tool handles them side by side rather than treating them as separate worlds — the difference is notation and tolerance classes, not geometry.
All the diameters reported are basic dimensions: the theoretical values from which tolerance classes are measured. A manufactured thread is never exactly at basic. External threads are made below it by an allowance and a tolerance, internal threads above it, which is what creates the clearance that lets a nut turn on a bolt at all.
How to Use It
- Choose the system to match your designation. M-something is metric; a fraction or number size with a thread count after a hyphen is Unified inch.
- Enter the two numbers from the designation. For M10×1.5 that is 10 and 1.5. For 1/4-20 that is 0.25 and 20.
- Set the number of starts if you are working with a multi-start thread. Almost every fastener is single start, where the lead equals the pitch.
- Add a length of engagement to see how many threads are actually in the joint, which matters far more than most people assume.
- For hole sizes, go to the clearance hole calculator instead. This page deliberately produces none.
The Formula and How It Is Calculated
Pitch and threads per inch are reciprocals with a unit conversion in between: pitch in mm = 25.4 ÷ TPI, and TPI = 25.4 ÷ pitch. An M10×1.5 thread is equivalent to 16.93 threads per inch; a 20 TPI inch thread has a pitch of 1.27 mm.
Everything else comes from the fundamental triangle, the sharp 60-degree V that the real thread form is truncated from. Its height is H = P × √3 ÷ 2 = 0.86603 P. The thread is truncated by H/8 at the crest and H/4 at the root, which puts the pitch line halfway up and gives:
Pitch diameter = D − 0.649519 × P and Minor diameter = D − 1.082532 × P, where D is the nominal major diameter. In inch units, substitute P = 1 ÷ TPI. The radial depth of engagement between mating threads is 5H/8 = 0.541266 × P.
Lead is pitch × number of starts, and the helix angle at the pitch diameter is arctan(lead ÷ (π × pitch diameter)). The number of threads in a joint is the length of engagement divided by the pitch.
Worked example: M10×1.5. The pitch diameter is 10 − 0.649519 × 1.5 = 9.0257 mm, the minor diameter is 10 − 1.082532 × 1.5 = 8.3762 mm, the radial depth is 0.8119 mm, and the fundamental triangle height is 1.2990 mm. The helix angle is arctan(1.5 ÷ (π × 9.0257)) = 3.028 degrees. Check it against 1/4-20: pitch is 0.05 inches, pitch diameter is 0.25 − 0.649519 × 0.05 = 0.21752 inches and minor diameter is 0.19587 inches — both of which match the basic values published in the inch thread standard.
Why the Pitch Diameter Is the Dimension That Matters
Fasteners do not bear on their crests or their roots. Loaded flanks contact each other around the pitch line, so the pitch diameter is what determines whether two threads actually fit, how much of the flank is in contact, and where a gauge measures. Tolerance classes — 6g and 6H in metric, 2A and 2B in inch — are defined as bands on the pitch diameter, not on the major diameter that appears in the designation.
That is why a bolt can measure correctly across the crests and still fail a ring gauge: the major diameter is a nominal reference while the pitch diameter carries the fit. The definitive geometry for the inch system is in ASME B1.1, Unified Inch Screw Threads, and for the metric M profile in ASME B1.13M, Metric Screw Threads: M Profile. Internationally the same profile is defined by ISO 68-1 for the basic profile and ISO 261 for the general purpose metric series; cite those by number when you need them, and read the tolerance classes from the standard rather than from any calculator.
A companion pitch diameter calculator also publishes on this site. Use that one when the pitch diameter itself is the whole question; use this page when you want the complete set of dimensions derived from a designation in one pass.
Coarse, Fine and Why the Pitch Is Not Free
The same nominal diameter comes in more than one pitch, and the choice changes real behaviour. A finer pitch gives a larger minor diameter and therefore a slightly larger tensile stress area, a shallower helix angle, and finer adjustment per turn. A coarser pitch is more tolerant of damage and dirt, assembles faster, and strips less readily in soft materials because each thread is bigger.
Read the numbers off the calculator with two different pitches at the same diameter and the trade-off is visible immediately: M10×1.5 has a minor diameter of 8.376 mm while M10×1.25 has 8.646 mm, a meaningful difference in the section carrying the load. The helix angle drops too, which is one of several factors in how a joint resists loosening — though vibration resistance depends on preload, surface condition and joint stiffness far more than on pitch alone. Preload and tightening torque are covered by our bolt torque calculator.
Threads in Engagement, and Why Six Is Usually Enough
The length of engagement field exists because of a counter-intuitive result: load is not shared evenly along a threaded joint. The first engaged thread carries a disproportionate share, and successive threads carry progressively less, so beyond roughly the first half-dozen threads the additional ones contribute very little to strength. Doubling engagement depth does not double the strength of the joint.
What extra engagement does buy is tolerance to damage and a margin against stripping in a soft parent material, which is exactly why tapped holes in aluminium are made deeper than the same thread in steel. It is also why thread inserts exist. None of that is decided by a calculator — it is a design judgement made with the material data and the joint's duty in front of you.
Reading and Writing a Designation
A metric designation is M, the nominal diameter, and then the pitch after a multiplication sign: M10×1.5. Where the pitch is omitted entirely, M10, the coarse-series pitch for that diameter is implied — and because that series is a published table rather than a formula, this page requires you to type the pitch rather than guessing it for you. Take it from the standard or measure it with a thread gauge.
An inch designation is the nominal size, a hyphen, and the threads per inch: 1/4-20 or 10-32. Numbered sizes below a quarter inch have their own diameter series, again a published table rather than a derivable formula. Enter the actual decimal diameter and the tool will do the rest. For related workshop geometry, the taper calculator handles tapered forms, the bolt circle calculator lays out hole patterns, and the spiral length calculator covers the flat spiral, which is a different curve from the helix a thread describes.
Arb Digital publishes free calculators for fasteners, machining, geometry and fabrication. Browse the library, or tell us what is missing.
Browse the free tools hub Contact Arb DigitalCommon Mistakes to Avoid
- Treating basic dimensions as manufacturing targets. Real threads are made to a tolerance class offset from basic; the numbers here are the reference those classes are measured from.
- Confusing pitch with lead. They are equal only on a single-start thread. On a two-start thread the lead is twice the pitch, and a nut advances twice as far per turn.
- Assuming a designation without a pitch is unambiguous. M10 implies the coarse-series pitch from a published table, which is why this tool asks for the number rather than inventing it.
- Using this page to size a hole. It produces no drill sizes at all. Tap drill and clearance hole sizing is a separate calculation with its own tolerances.
- Measuring the major diameter to check a fit. Fit is carried on the pitch diameter, and a thread can be correct across the crests while being well out of tolerance where it matters.
Related Free Tools From Arb Digital
For hole sizes — tap drill and clearance — use the clearance hole calculator. For tightening, the bolt torque calculator. For hole patterns, the bolt circle calculator. For tapered forms, the taper calculator, and for flat spirals rather than helices, the spiral length calculator. Everything else is in the free tools hub.
Frequently Asked Questions
Divide 25.4 by the pitch in millimetres, or divide 25.4 by the threads per inch to go the other way. A 1.5 mm pitch is 16.93 threads per inch, and 20 threads per inch is a pitch of 1.27 mm.
No, and that is deliberate. Tap drill and clearance hole sizing is a separate calculation with its own tolerances and target engagement, and it is handled by our clearance hole calculator, whose headline output is the tap drill diameter. This page derives the geometry of the thread form instead.
Subtract 0.649519 times the pitch from the nominal major diameter. For M10×1.5 that is 10 − 0.9743 = 9.0257 mm. The same constant applies to inch threads with the pitch taken as one divided by the threads per inch.
The diameter at the root of an external thread, or at the crest of an internal one. Basically it is the major diameter minus 1.082532 times the pitch, which puts M10×1.5 at 8.376 mm.
Pitch is the distance from one thread crest to the next. Lead is the distance the fastener advances in one full turn. They are the same on a single-start thread and differ by the number of starts on a multi-start one.
Because the coarse and fine pitch series for each nominal diameter are published tables, not formulas. Guessing a pitch from a diameter would mean reproducing a table from memory, and this page prefers to take the number from you or from the standard.
The 60-degree basic profile is shared, so the formulas for pitch diameter, minor diameter and thread depth are identical once pitch and threads per inch are related. The differences are in notation, the diameter and pitch series, and the tolerance class systems.
All dimensions produced by this tool are basic values derived from the theoretical 60-degree thread profile. They are not manufacturing dimensions. Tolerance classes, allowances, gauging practice and the published diameter and pitch series must be taken from the applicable standard, and fastener selection for any loaded joint is an engineering decision.
