Thread Calculator

Thread Calculator for Metric and Unified Fasteners

Use this thread calculator to estimate basic dimensions for common ISO metric and Unified screw threads. Choose the thread system and size, then select external thread for a bolt or screw, or internal thread for a nut or tapped hole. The calculator displays major diameter, pitch diameter, a basic minor diameter estimate, pitch in both unit systems, radial thread depth, and optional lead and helix angle for multi-start threads.

Metric threads are identified by a nominal diameter and pitch, such as M10 × 1.5. Unified inch threads are identified by nominal diameter and threads per inch, such as 1/2-13 UNC. Presets cover several common sizes, and custom inputs let you enter a different nominal diameter and pitch or TPI. All results are basic profile estimates, not manufacturing limits.

Thread dimensions are only one part of choosing a fastener. Tolerance class, fit, material, coating, load, engagement length, lubrication, and the matching nut or tapped hole also matter. Use the applicable drawing and thread standard for production or inspection. This calculator supports learning and preliminary checks; it does not certify a screw, bolt, nut, or threaded joint.

Thread Measurement Terms

The major diameter is the largest diameter of an external thread, measured across the crests. On an internal thread, the corresponding major diameter is the largest diameter of the internal thread form, near the thread roots. Nominal screw size usually refers to the basic major diameter, though actual manufactured dimensions have permitted limits.

The minor diameter is the smallest diameter of the thread. For an external thread, it is measured near the roots of the screw. For an internal thread, it is measured near the crests inside a nut or hole. The calculator uses basic profile formulas to estimate this dimension; actual crest truncation, root radius, tolerance, and fit may change the allowed values.

Pitch diameter is an imaginary cylinder through the thread where the width of a thread ridge and the width of the groove are equal. It is an important fit dimension because the mating threads engage along their flanks. Actual pitch diameter is controlled by the thread's tolerance class and can be measured with thread wires, gauges, or suitable metrology equipment.

Pitch is the distance along the axis from one thread crest to the next. Metric thread pitch is stated directly in millimeters. Unified inch threads use threads per inch (TPI), so pitch in inches is 1 divided by TPI. A higher TPI means a finer thread with a shorter distance between threads.

Basic 60-Degree Thread Formulas

ISO metric and Unified inch screw threads use a basic 60-degree thread form. The fundamental triangle height is H = 0.866025 × P, where P is pitch. The basic pitch diameter is approximately major diameter minus 0.649519 × P. For Unified threads, P in inches equals 1/TPI, so the same equation can be written as major diameter minus 0.649519/TPI.

For an ISO metric external thread, the basic external minor diameter estimate is major diameter minus 1.226869 × pitch. For a basic internal thread, the minor diameter is approximately major diameter minus 1.082532 × pitch. The radial depth is half the diameter difference: about 0.613435 × pitch for the external thread and 0.541266 × pitch for the internal thread.

For example, an M10 × 1.5 thread has a basic pitch diameter near 10 − (0.649519 × 1.5), or 9.0257 mm. The approximate external minor diameter is 10 − (1.226869 × 1.5), or 8.1597 mm. An internal thread's basic minor diameter estimate is 10 − (1.082532 × 1.5), or 8.3762 mm. Manufactured parts have tolerance limits around their basic dimensions.

For a 1/2-13 Unified thread, pitch is 1/13 inch, about 0.07692 inch. Its basic pitch diameter estimate is 0.5 − 0.649519/13, about 0.4500 inch. Use the appropriate standard tables for the actual tolerance class and series rather than treating these basic results as acceptance limits.

Metric Thread Sizes: Coarse and Fine Pitch

ISO metric fasteners use an M designation followed by nominal major diameter in millimeters. A pitch value may be written after the diameter, such as M8 × 1.25. Coarse pitch is commonly used for general fasteners, while fine pitch has a smaller distance between threads for the same nominal diameter. Fine threads can offer more precise adjustment and more thread engagement per length, but the correct choice depends on the application and design.

Common coarse metric presets in this calculator include sizes such as M3 × 0.5, M4 × 0.7, M5 × 0.8, M6 × 1.0, M8 × 1.25, M10 × 1.5, M12 × 1.75, M16 × 2.0, and M20 × 2.5. These are examples of common nominal combinations, not a complete list of available standard sizes. Fine-pitch options and special pitches should be entered using the drawing or supplier data.

When comparing metric and inch threads, convert pitch carefully. A pitch of 1.25 mm is not the same as 1.25 threads per inch. To convert metric pitch to TPI, divide 25.4 by pitch in millimeters. To convert TPI to metric pitch, divide 25.4 by TPI. The calculator shows both values to make comparisons easier.

Unified UNC and UNF Thread Sizes

Unified inch threads use a nominal diameter in inches and a threads-per-inch value. UNC means Unified National Coarse and UNF means Unified National Fine. A designation such as 3/8-16 UNC has a nominal diameter of 3/8 inch and 16 threads per inch. A 3/8-24 UNF thread uses the same nominal diameter with a finer pitch.

Small Unified screw sizes may use numbered diameters rather than a fractional inch size. The calculator's custom option accepts any positive major diameter and TPI, so you can enter a numbered screw's diameter from its standard reference or drawing. Do not guess the diameter from the screw number when the fastener must meet a specified class or standard.

UNC and UNF are not the only inch thread series. UNEF, constant-pitch series, pipe threads, and special threads have separate conventions and requirements. This calculator models a basic 60-degree Unified screw thread from diameter and TPI; it does not identify pipe thread taper, sealing behavior, special root forms, or a tolerance class.

Thread Lead and Helix Angle

Lead is the axial distance a screw advances in one complete turn. For a single-start thread, lead equals pitch. For a two-start thread, lead is twice pitch; for three starts, it is three times pitch. The calculator includes a thread-start input so you can estimate lead for a multi-start thread.

Helix angle is the angle of the thread helix at a selected reference diameter, often the pitch diameter. It can be estimated as arctan(lead ÷ (π × pitch diameter)). A larger lead or smaller pitch diameter creates a larger helix angle. This value helps describe screw motion, but it is not a strength rating or a substitute for a thread design check.

For ordinary single-start bolts, lead is normally the same as pitch. Multi-start threads are used when a larger linear movement per revolution is required. The thread form, engagement, self-locking behavior, and mating part must all be designed for the intended motion and load. Do not assume that a multi-start thread can replace a standard fastening thread without a full design review.

Internal and External Threads

An external thread is formed on the outside of a screw, bolt, or stud. An internal thread is formed inside a nut, insert, or tapped hole. Both use compatible pitch and thread form, but their tolerances and basic minor diameters differ. The thread class tells how much clearance or tolerance is permitted for a particular fit.

A loose fit may help with quick assembly or contaminated environments. A tighter fit may reduce play for a precision connection, but it demands closer manufacturing control. The class designation must come from the drawing, application standard, or fastener specification. A calculator using only nominal diameter and pitch cannot infer the required fit.

Coatings and plating can change effective dimensions and assembly feel. Material strength and engagement length also influence whether internal threads can carry the intended load. For a tapped hole in a softer material, a design may require more engagement, a thread insert, or a different fastener arrangement. Follow the application design rather than relying only on nominal size.

Coarse or Fine Thread: What to Check

Coarse and fine threads can share a nominal diameter while using different pitches. A coarse thread has a larger distance between crests; a fine thread has more crests in the same length. The choice can affect assembly speed, adjustment, engagement, resistance to cross-threading, and performance in a thin wall. There is no single pitch that is best for every use.

Before replacing a fastener with a different pitch, confirm that the mating nut or tapped hole has the matching thread. A coarse bolt will not correctly mate with a fine-pitch nut of the same nominal diameter. Also confirm that the thread series, class, material, finish, and specified length are appropriate for the joint.

For existing hardware, identify the thread from its marking, drawing, supplier data, or a suitable thread gauge. Measuring diameter alone is not enough to distinguish coarse from fine sizes or metric from Unified threads. If an unknown bolt is safety-related, avoid relying on a visual guess; identify the part and required standard first.

How to Use This Thread Calculator

Select ISO Metric or Unified Inch, then choose a common size preset or custom entry. For a preset, the calculator fills nominal major diameter and pitch or TPI. In custom mode, enter the dimensions from your drawing or fastener source. Select external for a bolt or screw, or internal for a nut or threaded hole.

Enter the number of thread starts if you want lead and helix angle. A normal single-start thread uses one start. Review the pitch diameter, minor diameter estimate, fundamental triangle height, radial depth, pitch conversion, and thread area at the minor diameter. The step-by-step section shows how the selected basic formulas are applied.

Use Save to keep the last result in the current browser, Copy to copy a summary, CSV to download the dimensions, or Print for a paper record. Keep the result with the correct size designation and source drawing. These basic dimensions do not include class-specific tolerance limits or inspection requirements.

Thread Calculator Limits and Common Mistakes

One common mistake is mixing TPI and metric pitch. TPI is a count per inch, while metric pitch is a length between adjacent crests. Another is using the external minor diameter formula for an internal thread. The calculator changes its minor-diameter estimate based on the selected thread type.

A basic diameter result is not an inspection limit. Real thread sizes are controlled by standard series, pitch diameter tolerance, major and minor diameter limits, allowances, and the selected class. Use the applicable standard tables, gauge instructions, and drawing for acceptance testing. A measured result outside a basic nominal value may still be acceptable within its tolerance, or it may fail a class-specific limit.

The calculator does not determine bolt preload, tensile strength, shear strength, fatigue life, stripping resistance, or joint capacity. It does not model pipe threads, buttress threads, Acme threads, metric trapezoidal threads, or other non-60-degree forms. Confirm the thread family before using a result, and seek qualified engineering guidance for load-bearing or safety-critical applications.