Thread Calculator uses D and P or TPI to calculate basic pitch diameter, root/minor diameter, pitch lead, TPI equivalent, and 60° thread geometry with H=0.866025P for metric and US screw threads.
This Thread Calculator computes the basic 60-degree thread profile geometry for both metric and US customary (inch) threads. Enter a nominal major diameter and thread pitch (or threads per inch), select the measurement system and thread application, and the calculator returns the basic pitch diameter, root and minor diameters, thread depth, pitch and lead data, cross-unit equivalents, fundamental triangle height, and truncation values — all from the standard analytical form of the 60-degree thread profile.
Results are theoretical basic dimensions at zero allowance. They are the starting reference for applying tolerance classes, allowances, and manufacturing limits per the relevant ISO or ASME standard.
What the Thread Calculator Measures
The coaxial cylinder at which thread tooth thickness equals groove width. Serves as the primary functional diameter for thread fit and the reference surface for pitch-diameter gauging.
The outer boundary of the root relief zone on external threads (bolts and screws). Defines the deepest extent of the thread form before the root radius is applied in production.
The minimum inner diameter of the thread form in nut and threaded-hole mode. Used as the basic reference for tap drill selection calculations (which are outside this tool's scope).
Pitch is the axial distance from one thread crest to the next. For single-start threads, lead equals pitch. Multi-start lead calculation is outside this tool's scope.
Converts the active pitch dimension to the opposite unit system. Metric mode shows the TPI equivalent; US mode shows the millimetre pitch equivalent. Useful for cross-referencing fastener catalogues.
The full height of the sharp theoretical V-profile before any crest or root truncation is applied. All derived depth dimensions are fractions of H.
The height removed from the theoretical sharp apex to form the flat or rounded crest. External threads use H/8 truncation; internal threads use H/4, producing the wider crest flat characteristic of nut profiles.
Thread Calculator Formulas
All expressions derive from the standard 60-degree symmetrical thread profile defined in ISO 68-1 and carried through ASME B1.1 / B1.13M. Variables are defined in the table below the formula cards.
Height of the complete sharp V formed by two flanks at 60°. The factor 0.866025 is (√3)/2, the exact trigonometric result for a 60-degree included half-angle.
Subtracts 3H/8 (= 0.324760P × 2 flanks) from the major diameter. Sets the theoretical cylinder of equal tooth and groove widths.
Removes 5H/8 from both flanks of the major diameter. Gives the nominal inner boundary of the thread form for external thread geometry.
Calculated as D minus 2h₃. Defines the maximum depth the root relief zone may reach on an external thread before it would encroach on the next thread form.
Radial distance from the major cylinder to the root boundary diameter d₃. Equals 17H/24 applied to a single radial direction.
The radial engagement depth of the thread form in a nut or threaded hole, measured from the major diameter downward. Equals 5H/8 minus the H/4 crest flat allowance.
Direct conversion from millimetre pitch to threads per inch using the inch-to-millimetre definition. Inverse gives P = 1/TPI for US mode entry.
| Symbol | Meaning | Unit |
|---|---|---|
| D | Nominal (major) diameter — calculator input | mm or in |
| P | Thread pitch — distance between adjacent crests | mm or in |
| TPI | Threads per inch — US customary pitch expression | 1/in |
| H | Fundamental triangle height of the sharp 60° V-profile | mm or in |
| E | Basic pitch diameter | mm or in |
| d₁ | Basic minor diameter for external thread geometry | mm or in |
| D₁ | Internal minor diameter — nut / threaded-hole mode | mm or in |
| d₃ | External root diameter | mm or in |
| h₃ | External radial root depth | mm or in |
| H₁ | Internal basic thread depth | mm or in |
Worked Example — M10 × 1.5 External Thread
The following shows the theoretical basic profile results for the calculator's default input values. All dimensions are basic (zero-allowance) values derived solely from the 60-degree form equations.
These are theoretical basic profile values at zero allowance. The ISO 6H/6g tolerance class for this thread size, for example, applies specific upper and lower deviations to the pitch diameter and minor diameter to produce the actual manufacturing limits for the bolt and nut — that step is outside the scope of this calculator.
Metric and US Customary Input Modes
Enter the nominal major diameter and thread pitch both in millimetres. The pitch input accepts any value, so this mode covers coarse, fine, and special pitches from the ISO metric series as well as non-standard pitches. The calculator uses P directly in all geometry expressions.
Results are returned in millimetres, with equivalent inch values shown in the unit-conversion card.
Enter the nominal major diameter in inches and the thread count as threads per inch (TPI). The calculator converts TPI to pitch distance internally using P = 1 / TPI before applying all 60-degree profile equations. Results are returned in inches, with equivalent millimetre values shown in the conversion card.
This mode covers Unified National (UNC, UNF, UNEF) and other 60-degree inch thread series. It does not verify whether the input TPI value corresponds to a listed series in ASME B1.1.
External and Internal Thread Mode
Applies to male threaded fasteners and threaded shafts. In this mode the root card reports the external root diameter d₃ and the associated radial root depth h₃. The d₃ dimension defines the deepest root-relief boundary permitted under the standard external thread form.
Truncation height is reported as H/8, corresponding to the theoretical crest flat of the external profile before root-radius or form relieving.
Applies to nuts, threaded inserts, and tapped holes. In this mode the root card reports the internal minor diameter D₁ and the basic thread depth H₁. D₁ is the theoretical minimum bore required for the internal form, and is the standard baseline reference prior to adding tolerance allowances.
Truncation height switches to H/4, reflecting the wider crest flat geometry characteristic of the internal 60-degree profile. Tap drill sizes are not calculated by this tool.
Calculator Scope and Limitations
This is a theoretical basic thread geometry calculator. It applies the standard 60-degree profile equations to the inputs provided and returns the nominal basic dimensions at zero allowance. It does not calculate, verify, or replace any of the following:
Outside This Calculator's Scope
- Tolerance class limits (e.g., 6H/6g, 2A/2B)
- Allowance (fundamental deviation)
- Maximum and minimum limit dimensions
- Plating or coating stock allowance
- Tap drill size
- Clearance hole size
- Over-wire / over-pin measurement
- Inspection pass/fail gauging
- Pitch-diameter correction for helix angle
- Multi-start thread lead calculation
Production threads must be specified and inspected against the applicable standard — ISO 965 for metric tolerance classes, ASME B1.1 for Unified inch threads, or the relevant shop or industry specification. The theoretical basic values from this calculator are the starting reference, not the finished tolerance band.
References
-
ISO 68-1:1998
ISO general purpose screw threads — Basic profile — Part 1: Metric screw threads.
Defines the 60-degree basic profile, H, pitch-diameter relationship, and truncation values for ISO metric threads.
iso.org — ISO 68-1 -
ASME B1.1-2003 (reaffirmed 2018)
Unified Inch Screw Threads (UN and UNR Thread Form).
Specifies the 60-degree Unified thread basic profile, series designations, and tolerance classes for inch fasteners.
asme.org — ASME B1.1 -
ASME B1.13M-2005 (reaffirmed 2015)
Metric Screw Threads: M Profile.
ASME adoption of the ISO metric thread profile; covers basic form, tolerances, and allowances for M-profile threads used in US practice.
asme.org — ASME B1.13M -
ISO 965-1:2013
ISO general purpose metric screw threads — Tolerances — Part 1: Principles and basic data.
The companion tolerance standard to ISO 68-1; defines deviation classes (e.g., 6H, 6g) applied to the basic profile dimensions.
iso.org — ISO 965-1 -
NIST — Engineering Metrology Toolbox
Length and dimensional measurement resources and unit conversion references.
emtoolbox.nist.gov