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. Use it as a metric thread calculator by entering nominal diameter and pitch in millimetres, or switch to US mode to use it as a TPI calculator — enter threads per inch and the tool converts to pitch internally.
As a thread pitch calculator it returns basic pitch diameter, root and minor diameters, and lead data from either input. Select External for a bolt or screw thread, or use it as an internal thread calculator for nut and tapped-hole geometry — the root and depth outputs switch automatically to match.
Results are theoretical basic dimensions at zero allowance, the standard starting reference before tolerance classes and allowances are applied.
Standard thread size reference table
Basic (zero-allowance) dimensions for common standard thread sizes, calculated with the same formulas used above. For a size not listed here, or a non-standard pitch, enter it directly into the calculator.
ISO metric coarse series (external / bolt)
| Size | Pitch | Pitch diameter (E) | Root diameter (d₃) | Minor diameter (d₁) | TPI equivalent |
|---|---|---|---|---|---|
| M3 | 0.5 mm | 2.675 mm | 2.387 mm | 2.459 mm | 50.80 |
| M4 | 0.7 mm | 3.545 mm | 3.141 mm | 3.242 mm | 36.29 |
| M5 | 0.8 mm | 4.480 mm | 4.019 mm | 4.134 mm | 31.75 |
| M6 | 1.0 mm | 5.350 mm | 4.773 mm | 4.917 mm | 25.40 |
| M8 | 1.25 mm | 7.188 mm | 6.466 mm | 6.647 mm | 20.32 |
| M10 | 1.5 mm | 9.026 mm | 8.160 mm | 8.376 mm | 16.93 |
| M12 | 1.75 mm | 10.863 mm | 9.853 mm | 10.106 mm | 14.51 |
| M16 | 2.0 mm | 14.701 mm | 13.546 mm | 13.835 mm | 12.70 |
| M20 | 2.5 mm | 18.376 mm | 16.933 mm | 17.294 mm | 10.16 |
UNC — Unified National Coarse (external / bolt)
| Size | TPI | Pitch | Pitch diameter (E) | Root diameter (d₃) | Minor diameter (d₁) |
|---|---|---|---|---|---|
| 1/4-20 | 20 | 0.0500 in (1.270 mm) | 0.2175 in | 0.1887 in | 0.1959 in |
| 5/16-18 | 18 | 0.0556 in (1.411 mm) | 0.2764 in | 0.2443 in | 0.2524 in |
| 3/8-16 | 16 | 0.0625 in (1.587 mm) | 0.3344 in | 0.2983 in | 0.3073 in |
| 7/16-14 | 14 | 0.0714 in (1.814 mm) | 0.3911 in | 0.3499 in | 0.3602 in |
| 1/2-13 | 13 | 0.0769 in (1.954 mm) | 0.4500 in | 0.4056 in | 0.4167 in |
UNF — Unified National Fine (external / bolt)
| Size | TPI | Pitch | Pitch diameter (E) | Root diameter (d₃) | Minor diameter (d₁) |
|---|---|---|---|---|---|
| 1/4-28 | 28 | 0.0357 in (0.907 mm) | 0.2268 in | 0.2062 in | 0.2113 in |
| 5/16-24 | 24 | 0.0417 in (1.058 mm) | 0.2854 in | 0.2614 in | 0.2674 in |
| 3/8-24 | 24 | 0.0417 in (1.058 mm) | 0.3479 in | 0.3239 in | 0.3299 in |
| 1/2-20 | 20 | 0.0500 in (1.270 mm) | 0.4675 in | 0.4387 in | 0.4459 in |
What the Thread Calculator Measures
Basic Pitch Diameter
E = D − 0.649519P
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.
External Root Diameter (d₃)
d₃ = D − 1.226869P
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.
Internal Minor Diameter (D₁)
D₁ = D − 1.082532P
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).
Thread Pitch and Single-Start Lead
P (mm) or 1/TPI (in)
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.
TPI Equivalent / Pitch Equivalent
TPI = 25.4 / P
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.
Fundamental Triangle Height (H)
H = 0.866025P
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.
Truncation Height
H/8 (external) · H/4 (internal)
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.
| Formula | Name | Notes |
|---|---|---|
H = 0.866025 × P | Fundamental Triangle Height | Height of the complete sharp V. The factor 0.866025 is (√3)/2, the exact trigonometric result for a 60-degree included half-angle. |
E = D − 0.649519P | Basic Pitch Diameter | Subtracts 3H/8 from the major diameter. Sets the theoretical cylinder of equal tooth and groove widths. |
d₁ = D − 1.082532P | Basic Minor Diameter | Removes 5H/8 from both flanks of the major diameter. Gives the nominal inner boundary of the thread form for external thread geometry. |
d₃ = D − 1.226869P | External Root Diameter | Calculated as D minus 2h₃. Defines the maximum depth the root relief zone may reach on an external thread. |
h₃ = 0.613435P | External Radial Root Depth | Radial distance from the major cylinder to the root boundary diameter d₃. Equals 17H/24 applied to a single radial direction. |
H₁ = 0.541266P | Internal Basic Thread Depth | Radial engagement depth of the thread form in a nut or threaded hole. Equals 5H/8 minus the H/4 crest flat allowance. |
P = 1 / TPI | Pitch from TPI (US mode) | Converts threads per inch to pitch distance in inches before applying all profile equations. |
TPI = 25.4 / P | TPI from Metric Pitch | Direct conversion from millimetre pitch to threads per inch using the inch-to-millimetre definition. |
Variable Legend
| 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 from the 60-degree form equations.
Inputs: System: Metric (mm) · Application: External (Bolt / Screw) · D = 10.000 mm · P = 1.500 mm
| Output | Value |
|---|---|
| Basic Pitch Diameter | 9.026 mm |
| External Root Diameter (d₃) | 8.160 mm |
| Radial Root Depth (h₃) | 0.920 mm |
| Basic Minor Diameter (d₁) | 8.376 mm |
| Thread Pitch (P) | 1.500 mm |
| Single-Start Lead | Same as pitch |
| TPI Equivalent | 16.933 TPI |
| Nominal Diameter (in) | 0.394 in |
| Equivalent Pitch (in) | 0.059 in |
| Equivalent Pitch Diameter (in) | 0.355 in |
| Fundamental Triangle (H) | 1.299 mm |
| Truncation Height | 0.162 mm |
These are theoretical basic profile values at zero allowance. The ISO 6H/6g tolerance class for this thread size applies specific upper and lower deviations to the pitch diameter and minor diameter to produce the actual manufacturing limits for bolt and nut — that step is outside the scope of this calculator.
Metric and US Customary Input Modes
Metric Mode (mm)
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 output.
US Customary Mode (inch)
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 output. 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
External — Bolt / Screw
Applies to male threaded fasteners and threaded shafts. In this mode the root output 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.
Internal — Nut / Hole
Applies to nuts, threaded inserts, and tapped holes. In this mode the root output 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.
Frequently Asked Questions
How do you calculate thread pitch diameter?
Basic pitch diameter equals the major diameter minus 0.649519 times the pitch: E = D − 0.649519P. For a metric M10 × 1.5 thread, that’s 10 − (0.649519 × 1.5) = 9.026 mm. The constant 0.649519 comes from 3H/8, where H is the fundamental triangle height of the 60° thread profile.
How do you calculate thread depth?
Thread depth depends on whether it’s an external or internal thread. For an external thread (bolt/screw), radial root depth is h₃ = 0.613435P. For an internal thread (nut/hole), basic thread depth is H₁ = 0.541266P. A 1.5 mm pitch external thread has a root depth of 0.920 mm; the same pitch on an internal thread has a depth of 0.812 mm.
What is the TPI formula for a thread?
TPI (threads per inch) equals 25.4 divided by the pitch in millimetres: TPI = 25.4 / P. A 1.5 mm pitch converts to 16.93 TPI. Going the other direction — from TPI to pitch — divide 1 by the TPI value: a 20 TPI thread has a pitch of 0.05 inches (1.27 mm).
What is 12 TPI thread depth in mm?
A 12 TPI thread has a pitch of 2.117 mm. On an external thread, the radial root depth works out to 1.298 mm; on an internal thread, the basic depth is 1.146 mm. This comes from converting TPI to pitch first (P = 1/TPI = 0.0833 in = 2.117 mm), then applying the depth formula for the relevant thread type.
How do you calculate threads per inch from pitch?
Divide 25.4 by the pitch in millimetres, or divide 1 by the pitch in inches — both give threads per inch. For example, a 1.25 mm pitch converts to 20.32 TPI, and a thread with a 0.05-inch pitch is exactly 20 TPI.
What is thread root diameter?
Root diameter is the smallest diameter of the thread form, measured at the base of the groove. It’s calculated differently for external and internal threads: external root diameter is d₃ = D − 1.226869P, while internal minor diameter is D₁ = D − 1.082532P — the internal value is larger because it’s measured to a shallower depth (H/4 truncation vs H/8 for external).
Does this calculator include thread tolerance classes (6H/6g, 2A/2B)?
No — this calculator returns theoretical basic dimensions at zero allowance, not the toleranced manufacturing limits. Basic dimensions are the reference point tolerance classes are applied to, not a substitute for them. For actual production limits, apply the relevant tolerance class from ISO 965-1 (metric) or ASME B1.1 (Unified inch) to the basic values shown here.
How do you convert a metric thread to its nearest TPI equivalent?
Divide 25.4 by the metric pitch in millimetres. A common coarse M10 × 1.5 thread converts to 16.93 TPI — close to, but not exactly matching, any standard UN inch series, since metric and inch thread series aren’t designed to align. The calculator’s “Nominal Diameter Eq.” and “TPI Equivalent” outputs give this conversion automatically for any input.
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. The following are outside its 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