Thread Calculator
Calculate basic ISO metric or Unified 60° thread dimensions, pitch, lead and an approximate cut-tap drill diameter.
For informational use only; basic dimensions are not tolerance-class limits or inspection approval. Terms and Conditions
Basic nominal geometry; manufacturing limits depend on the thread standard and class.
Choose your thread
Use a listed thread or enter custom major diameter and pitch. Changing either dimension switches the size to Custom.
Thread dimensions
Basic geometry only; not inspection tolerances.
Related dimensions
- Calculating—
Show calculation stepsView the formula, substitutions and limitations
- Enter valid inputs.
Thread profile
Conceptual axial section of one 60° thread; actual manufacturing crest and root profiles differ by standard.
Blue dashed: major reference · Amber dashed: pitch reference · Green dashed: minor reference. P is axial thread pitch.
Dimension values are listed above; visual is illustrative, not to scale.
Method, sources and assumptions
Theoretical 60° geometry, scope and necessary verification.
ISO metric and Unified basic 60° geometry; selected tolerance classes are reference labels only. This tool does not calculate manufacturing dimensional limits, gauges, or strength.
- Illustrative M10 × 1.5 basic geometry is preloaded; verify actual manufacturing requirements using applicable standards and tooling data.
Calculator guide
What the Thread Calculator Tells You
The Thread Calculator above calculates basic dimensions of a 60° ISO metric or Unified inch screw thread from its nominal major diameter and pitch (or threads per inch). Select an internal or external thread to obtain its corresponding basic pitch and minor/root diameters; you can also calculate thread lead and an approximate internal cut-tap drill diameter. The answers describe geometry, not permissible manufacturing tolerances.
For an M10 × 1.5 thread, the basic pitch diameter is approximately 9.026 mm. Its basic internal minor diameter is approximately 8.376 mm, while its basic external root diameter is approximately 8.160 mm. Choosing the correct thread form is therefore as important as choosing the nominal size.
- Known inputs
- Major diameter and pitch or TPI
- Primary output
- Your selected basic dimension, lead or cut-tap estimate
- Key limitation
- No minimum/maximum tolerance-class or inspection limits
How to Use the Thread Calculator
Choose the thread specification first, then choose the result you need. The calculator starts with illustrative M10 × 1.5 values, which should be replaced with your actual thread information.
Select the thread standard and size
Choose ISO metric or Unified inch and a listed nominal thread size. You can also enter a custom major diameter and pitch; editing either dimension changes the size selection to Custom. A custom combination is not necessarily a recognized standard thread.
Choose the thread form and primary result
Select External (bolt) for a male thread or Internal (tapped hole) for a female thread. Then select basic pitch diameter, basic minor/root diameter, thread lead or, for internal threads only, the cut-tap drill estimate. The latter is unavailable for an external thread.
Check units and advanced settings
Diameter may be entered in mm or inches; pitch may be expressed as mm pitch, inch pitch or TPI. Advanced options include number of starts, result units, a reference-only thread-class label and, for internal threads, cut-tap target percentage. The class label does not calculate class limits.
Read the result and its context
Read the selected primary result first, then use Related dimensions and Show calculation steps to see the other geometric values and substitutions. Check the displayed thread form and units before using a dimension in a drawing, machining plan or inspection procedure.
Which Thread Diameter Do You Need?
Major, pitch and minor diameter describe different reference surfaces. An internal thread and an external thread have different minor-diameter locations, even when they share the same nominal diameter and pitch.
- Nominal major diameter
- The designated thread size: 10 mm for M10 or 0.250 in for a 1/4-inch Unified thread. For a male thread, the major diameter is the outer crest reference; the matching female thread uses the same basic nominal major diameter.
- Basic pitch diameter
- The diameter of an imaginary coaxial cylinder intersecting the profile where the ideal thread and groove widths are equal. This is a geometric reference, not a pass/fail gage result.
- Basic internal minor diameter
- The diameter at the internal-thread crests, toward the center of a tapped hole. It is not the nominal predrill diameter for every tapping process.
- Basic external root diameter
- The diameter at the roots of the male thread. For Unified external threads, the calculator labels this as a geometric reference; actual UN/UNR root geometry must be checked separately.
- Pitch and TPI
- Pitch is the axial distance between corresponding points on adjacent thread forms; TPI counts threads per inch. A 20-TPI thread has 0.050 in pitch, or 1.27 mm.
- Lead
- Axial advance in one complete revolution. Lead equals pitch for one start; with multiple starts, lead equals pitch multiplied by the number of starts.
External thread (bolt)
M10 × 1.5: nominal major Ø 10.000 mm → basic pitch Ø 9.026 mm → basic external root Ø 8.160 mm.
Internal thread (tapped hole)
M10 × 1.5: nominal major Ø 10.000 mm → basic pitch Ø 9.026 mm → basic internal minor Ø 8.376 mm. A predrill is selected separately.
Thread Dimensions, Pitch and Lead Formulas
The calculator uses geometric relationships for a nominal 60° thread. Pitch diameter is obtained by subtracting a pitch-dependent offset from nominal major diameter. The applicable internal minor or external-root relationship is then selected by thread form.
Basic pitch diameter
Basic pitch diameter = nominal major diameter − 0.64951905 × axial pitch. Lowercase symbols identify external threads; uppercase symbols identify internal threads.
ISO metric internal minor and external root references
The internal minor-diameter offset and external root-diameter offset are different. The Unified external-root output is a simplified nominal 60° reference, not a complete UN/UNR root-profile or tolerance calculation.
Pitch, TPI and lead
Divide 25.4 by threads per inch to obtain pitch in millimeters. Multiply pitch by the number of starts to obtain lead; pitch and lead are equal for a single-start thread.
- \(d\)
- External nominal major diameterDiameter used for the nominal male thread size.
- \(D\)
- Internal nominal major diameterBasic nominal size of the female thread.
- \(d_2\)
- Basic external pitch diameterPitch-cylinder reference of the nominal male profile.
- \(D_2\)
- Basic internal pitch diameterPitch-cylinder reference for the nominal female-thread profile.
- \(D_1\)
- Basic internal minor diameterFemale-thread crest diameter under the metric basic-profile relationship.
- \(d_3\)
- Basic external root diameterMetric design-profile root diameter; simplified reference when the tool is set to Unified.
- \(P\)
- Axial thread pitchDistance between corresponding points on adjacent thread forms.
- \(L\)
- Thread leadAxial advance per complete revolution.
- \(n\)
- Number of startsIndependent helical threads around the same axis.
- \(\mathrm{TPI}\)
- Threads per inchReciprocal of pitch measured in inches.
Worked Example: M10 × 1.5 Thread
Consider a single-start, standard-size M10 × 1.5 metric thread. Calculate its basic pitch diameter, compare its internal and external minor/root references, and check its single-start lead.
Substitute the values
The nominal pitch-diameter offset is 0.974278575 mm, leaving 9.025721425 mm.
Basic geometry results
Pitch diameter: 9.026 mm
Internal minor diameter: 8.376 mm
External root diameter: 8.160 mm
Single-start lead: 1.500 mm/rev
Use the internal value to describe a female thread’s basic crest diameter and the external value for the male thread’s basic root reference; do not substitute one for the other.
Worked Example: 1/4-20 UNC Thread
A 1/4-20 UNC single-start thread has nominal major diameter 0.250 in and 20 threads per inch. Choose Unified inch and the 1/4-20 UNC size in the calculator to obtain basic geometry; the 2A/2B class labels do not generate manufacturing limits.
Convert pitch and substitute
Converted pitch: 0.050 in × 25.4 = 1.270 mm. The unrounded basic pitch diameter is 0.2175240475 in.
Basic geometric result
Pitch diameter ≈ 0.2175 in (5.525 mm)
Single-start lead = 0.050 in/rev (1.270 mm/rev)
These values do not establish a finished 2A or 2B thread’s acceptable diameter range.
How to Interpret and Check Your Result
A basic diameter is a geometric reference used to understand a thread profile. Before using it in a drawing or machining operation, verify whether you need the basic dimension, an actual measured dimension, a finished tolerance limit or a tool-selection diameter.
What the number means
For M10 × 1.5, 9.026 mm is the basic pitch-cylinder diameter. It is neither a recommended predrill diameter nor proof that an actual external or internal thread fits its mate.
What changing pitch does
With major diameter fixed, increasing pitch by 0.1 mm reduces basic pitch diameter by about 0.06495 mm. For M10, changing pitch from 1.5 to 1.25 mm increases the calculated basic pitch diameter from about 9.026 to 9.188 mm.
Fast sanity check
For a valid positive 60° nominal profile, calculated pitch and minor/root diameters must remain positive and below nominal major diameter. If a result seems too small, confirm that you entered a pitch rather than a TPI number in a pitch-unit field.
Units describe the same thread
10.000 mm = 0.393701 in; a 1.500 mm pitch = 0.059055 in pitch = 16.933 TPI. Switching units changes the displayed number, not the physical diameter or pitch. Similar pitch alone does not make inch and metric designations interchangeable.
Pitch versus multi-start lead
With pitch held at 2 mm, one start gives 2 mm/rev lead; three starts give 6 mm/rev. Number of starts changes lead, not the adjacent-turn pitch or basic pitch diameter.
Identify an Unknown Thread
If you do not know the designation, measure both the outside diameter and pitch or TPI before choosing a standard size. A close match identifies a candidate, not a verified fit class or safe interchangeability.
Measure the major diameter
Use calipers across accessible external crests, or consult a correctly identified mating-thread drawing for an internal thread. Worn crests, plating and measurement uncertainty can shift the reading.
Measure pitch independently
Use a thread pitch gauge or measure several adjacent intervals and divide by the number of intervals. For an inch thread, TPI = 1 ÷ pitch measured in inches. An external diameter near 10 mm does not establish whether the thread is M10 × 1.5 or M10 × 1.25.
Compare candidate designations
Match the measured diameter and pitch against an appropriate ISO metric or Unified reference, then check thread angle, hand, mating component and required class. This calculator computes geometry from a chosen size; it does not automatically identify an unknown thread.
| Designation | Nominal major Ø | Pitch | Basic pitch Ø |
|---|---|---|---|
| M8 × 1.25 | 8.000 mm | 1.250 mm | 7.188 mm |
| M10 × 1.5 | 10.000 mm | 1.500 mm | 9.026 mm |
| 1/4-20 UNC | 0.250 in | 0.050 in (20 TPI) | 0.2175 in |
Using the Result for Tap Drilling
An internal-thread cut-tap drill estimate gives a theoretical starting-hole diameter. It is not the basic internal minor diameter and does not by itself establish a compliant finished thread.
Simplified 60° cut-tap relationship
Starting drill diameter ≈ nominal major diameter − 1.299038 × pitch × target thread percentage divided by 100. Here, T is the selected cut-tap target percentage, not a tolerance class or measured engagement length.
This is a simplified internal cut-tapping estimate. A form tap needs its own tooling-specific predrill recommendation.
Calculated target
For M10 × 1.5 at 75% nominal thread, the estimate is 10 − 1.299038 × 1.5 × 0.75 ≈ 8.539 mm. This value is a theoretical starting point, not a claim that an 8.539 mm production drill is stocked or required.
Actual drill and finished thread
Compare the theoretical target against available drill sizes, tap-maker guidance, workpiece material and the required finished internal-thread geometry. Confirm the actual drilled hole and finished thread by the applicable inspection method. Do not infer pass/fail solely from the approximate percentage.
Reverse check for an 8.5 mm drill
If a cut tap uses an actual 8.5 mm starting hole for M10 × 1.5, invert the same approximation:
A slightly smaller starting hole than the 8.539 mm theoretical target corresponds to a slightly higher approximate percentage. This does not establish actual finished-thread compliance.
Common Thread Calculation Mistakes
The most consequential mistakes come from mixing thread forms, confusing units or applying basic geometry as though it were a finished-part specification.
Entering TPI as millimeter pitch
For 1/4-20 UNC, enter 20 with the TPI unit selected, or enter 1.27 with mm pitch selected. Entering 20 as millimeters of pitch describes a completely different, invalid thread geometry for a 1/4-inch diameter.
Using the external root as a tap hole
For M10 × 1.5, 8.160 mm is the basic external root diameter, not the internal thread’s basic minor diameter and not the cut-tap drill target. Choose Internal before reading the female-thread geometry.
Confusing pitch with lead
A three-start thread with 2 mm pitch has 6 mm/rev lead. If the advance per revolution matters, select the lead result and set the actual number of starts in Advanced options.
Assuming a thread class changes this result
The tool’s 6g, 6H, 2A and 2B selections are descriptive labels. They do not apply deviations, allowances or minimum/maximum limits to the displayed basic geometry.
Using a 60° equation for another profile
NPT tapered threads, BSP Whitworth forms, ACME and metric trapezoidal threads have distinct profiles or dimensional conventions. Do not interpret a custom 60° calculation as a complete result for these thread families.
Treating displayed decimals as manufacturing precision
Three decimal places may be useful for comparing calculated basic values, but the measured accuracy, permissible dimensional limits and appropriate rounding for production must be established separately.
Calculation Scope and Manufacturing Limits
The formulas model nominal 60° thread geometry, plus a simplified internal cut-tapping estimate. They do not simulate the complete manufactured thread or certify a part for use.
Basic geometry is not a tolerance interval
A class designation requires standard-specific fundamental deviations, allowances and tolerances to calculate finished limits. The calculator does not implement those calculations or gaging criteria.
Unified external root is a reference
The calculator’s Unified external root uses a simplified 60° expression; UN and UNR design roots can differ in shape and permitted dimensions. Refer to ASME B1.1 for the actual selected profile and class.
Custom dimensions need independent qualification
A mathematically valid major diameter and pitch are not necessarily an ISO or Unified standard designation. Confirm availability, mating compatibility, strength and manufacturing requirements before specifying a custom thread.
No mechanical strength or joint verification
The tool does not calculate stripping strength, stress area, bolt preload, fatigue, engagement suitability or sealing. Those require additional design inputs and methods.
Engineering Standards and Method References
These standards establish the metric and Unified profile and dimensional frameworks behind the terminology used here. Their public catalog pages describe scope; production-critical dimensional limits require the applicable full standard.
- ISO 68-1:2023 — ISO general purpose screw threads: metric basic and design profiles — Describes the metric fastening-thread basic and design profile scope.
- ISO 724:2023 — ISO general purpose metric screw threads: basic dimensions — Defines the basic-dimension framework for metric fastening screw threads.
- ASME B1.1-2024 — Unified Inch Screw Threads — Governs Unified thread forms, series, classes, allowances and tolerances; consult the full standard for production limits and root profiles.
Numerical example check: the pitch-diameter equation was rearranged to recover the original nominal diameter. Rounded example values are basic geometric references, not values from a class-dependent tolerance table.
Thread Calculator FAQs
What does M10 × 1.5 mean?
M identifies an ISO metric screw thread, 10 is its nominal major diameter in millimeters and 1.5 is its axial pitch in millimeters. A mating part must have the appropriate compatible thread specification, not merely the same nominal diameter.
What is the pitch of a 1/4-20 UNC thread?
It has 20 threads per inch, so pitch is 1/20 = 0.050 in, equivalent to 1.270 mm. The 1/4 designation means a nominal major diameter of 0.250 in.
Why are internal and external minor diameters different?
The two basic profiles have different crest/root truncations. For M10 × 1.5, the basic internal minor diameter is about 8.376 mm and the basic external root diameter is about 8.160 mm. Use the thread-form control to select the relevant one.
Does selecting 6H or 2B give me a finished thread limit?
No. Those are reference-only class labels in this calculator. Minimum and maximum allowable diameters and the required inspection criteria must be established from the applicable full thread standard.
Can the cut-tap estimate be used for a forming tap?
No. Form tapping displaces material rather than removing it in the same way as a cutting tap. Follow the specific form-tap manufacturer’s hole-size recommendation for the tooling, material and thread requirements.
Can the calculator identify an unknown bolt from one diameter measurement?
No. Measure both major diameter and pitch/TPI, compare the candidate designation and examine thread form and fit requirements. Similar measured diameters can occur in distinct thread standards or sizes.
What is the difference between UNC and UNF?
UNC and UNF are different Unified inch thread series. For example, 1/4-20 UNC has 20 TPI, while 1/4-28 UNF has 28 TPI; equal nominal major diameters do not make them interchangeable.
Can I use these formulas for NPT, BSP or ACME threads?
No. Tapered pipe, Whitworth-profile and ACME threads use different profiles or designation rules. A custom 60° result is not a substitute for the applicable thread standard.