Thread Calculator

Thread Calculator for UNC, UNF and ISO metric bolt and nut limits by class, pitch and minor diameter, tap drill size, three-wire reading and stress area, or match a measured screw.

How a Thread Calculator Sizes a 60° Thread

A thread calculator works out every diameter of a screw thread from two numbers: the nominal size and the pitch. Unified inch (UN) and ISO metric threads share the same 60° profile, so one set of formulas covers both.

The nominal diameter is the size a thread is named by, such as 1/4 in or 6 mm. It equals the basic major diameter, the largest diameter measured across the crests of a bolt.

Pitch is the distance from one crest to the next. Inch threads give it as threads per inch (TPI), so the pitch is 1 ÷ TPI. Metric threads state the pitch in millimeters, as in M6 × 1.

To calculate a 60° thread, start from the sharp V triangle the profile is cut from. Its height sets every other depth on the thread.

$$H=0.866025\times P$$

H is the height of the sharp V and P is the pitch. The real thread is flattened at the crest and root, so the working depth is a fraction of H.

Pitch Diameter and Minor Diameter Formulas

To calculate the pitch diameter of a thread, subtract 0.649519 times the pitch from the major diameter. The pitch diameter is where the thread groove and the thread ridge have equal width.

$$E=D-0.649519\times P$$

To calculate the minor diameter, subtract 1.082532 times the pitch. That is the basic minor diameter of the nut thread, the bore a tap drill aims for.

$$D_1=D-1.082532\times P$$

A metric bolt root sits a little deeper, at d₃ = d - 1.226869 × P, because the bolt root is rounded. Every thread calculator uses these constants, which come from the basic profile shared by ASME B1.1 and the ISO metric standards.

Worked Example: 1/4-20 UNC

Run a 1/4-20 UNC through a thread calculator and it starts from D = 0.250 in and P = 1 ÷ 20 = 0.050 in. The sharp V height is 0.866025 × 0.050 = 0.0433 in.

The basic pitch diameter is 0.250 - 0.649519 × 0.050 = 0.2175 in. The basic minor diameter is 0.250 - 1.082532 × 0.050 = 0.1959 in, which is where the nut thread's minor band starts.

Metric Thread Calculator Sizes in mm

To calculate metric thread size, read the callout. M10 × 1.5 means a 10 mm nominal diameter with a 1.5 mm pitch. A coarse thread often drops the pitch, so plain M10 means M10 × 1.5.

A thread calculator in mm runs the same formulas with millimeters. The table gives the ISO 965-1 limits for the common 6g bolt and 6H nut fit, worked from the tool's own tolerance tables.

So what is the diameter of an M6 thread? A metric thread calculator gives more than one answer.

The nominal major diameter is 6 mm, but a 6g bolt measures 5.794 to 5.974 mm across the crests. Its pitch diameter runs 5.212 to 5.324 mm, and the 6H nut minor runs 4.917 to 5.153 mm.

A metric thread diameter calculator never gives the full nominal size on a bolt. The 6g position pulls every bolt diameter slightly under nominal, which leaves room for plating and easy assembly.

Bolt Thread Calculator: Classes and Limits

A bolt thread calculator turns the basic sizes into a min and max for each diameter. The class decides how far below basic the bolt sits and how wide its tolerance band is.

UN bolts use classes 1A, 2A and 3A under ASME B1.1. Class 2A is the general fit, and the one to pick in a thread calculator unless the print says otherwise.

Class 2A takes a small allowance off the pitch diameter, 0.3 times the 2A pitch diameter tolerance, so plated parts still assemble.

Class 1A is the loose fit, at 1.5 times the 2A tolerance with the same allowance. Class 3A has no allowance and 0.75 times the tolerance, for close-fit and precision work.

ISO metric threads name the fit by a grade and a letter. In 6g, the 6 sets the tolerance width and the g sets a small gap below basic. The 4h class has no gap, and 6e leaves a larger gap for thick plating.

The pitch diameter tolerance for a 2A thread follows one ASME formula, which a thread calculator applies with the major diameter as the length of engagement. For 1/4-20 it gives 0.0037 in, which sets the 0.2127 to 0.2164 in band in the table.

$$T_{d2}=0.0015D^{1/3}+0.0015\sqrt{D}+0.015P^{2/3}$$

D and P are in inches. Class 2B nuts take 1.3 times this value, 1B nuts 1.95 times and 3B nuts 0.975 times.

Internal Thread Calculator for Nuts and Tapped Holes

An internal thread calculator works in the other direction. The nut thread starts at the basic size and its tolerance runs larger, so a nut never cuts under the basic pitch or minor diameter.

The minor diameter band is the size that matters most in the shop, because it is the hole your tap drill leaves. A 1/4-20 2B nut allows 0.1959 to 0.2074 in, and an M6 6H nut allows 4.917 to 5.153 mm.

Minimum Thread Engagement

How deep a tapped hole must be depends on stripping. Machinery's Handbook gives the shortest engagement at which a bolt breaks before its threads strip, when the nut and bolt are the same strength.

$$L_e=\frac{2A_s}{\pi K_{n,max}\left(0.5+0.57735n(E_{s,min}-K_{n,max})\right)}$$

A_s is the tensile stress area, K_n,max is the largest nut minor diameter, E_s,min is the smallest bolt pitch diameter and n is threads per inch. For 1/4-20 that is 0.174 in, about 0.70 times the diameter or 3.5 threads.

A thread calculator gives this as the floor for a steel nut. A softer tapped part needs more engagement than this, since its threads strip first. The Bolt Pull Out Force Calculator checks strip strength in a weaker material.

Tap Drill Size From Thread Percentage

A tap drill rarely cuts a 100% thread. Most shops aim for about 75%, which keeps nearly all the strength while making the tap far easier to turn. A thread calculator trades that percentage against drill size, since a lower percentage means a bigger drill.

$$Drill=D-\frac{\%\times 1.299038}{100\times TPI}$$

D is the major diameter in inches and % is the thread percentage. For metric threads, replace 1 ÷ TPI with the pitch in millimeters. A 1/4-20 at 75% needs 0.250 - 0.75 × 1.299038 × 0.050 = 0.2013 in, which is a #7 drill.

A roll form tap pushes metal into the thread instead of cutting it, so it needs a larger hole. The same formula uses 0.68 in place of 1.299038. A HomemadeTools forum member who writes drill software uses the same 0.0068 factor.

Check the stock drill against the class minor band before you drill. A drill that leaves a hole under the band makes a high thread percentage, which raises tap breakage in tough metals. One over the band fails the GO gauge on the minor.

Holes for clearance rather than threads use a different chart. The Clearance Hole Calculator sizes those, and the Countersink Depth Calculator handles flat head screw seats.

Thread Gauge Calculator: Wires and GO / NOT GO

Pitch diameter is hard to measure with calipers, so shops check it over three wires. Each wire sits in a thread groove, and a micrometer reads across them.

$$M=E+3W-0.866025\times P$$

M is the reading over the wires, E is the pitch diameter and W is the wire size. The best wire, W = 0.57735 × P, touches the flanks right at the pitch diameter, and the formula then reduces to M = E + H.

For 1/4-20 UNC 2A, the best wire is 0.0289 in and the reading should fall from 0.2560 to 0.2597 in. Wires from 0.505 × P to 1.01 × P still sit on the flanks if the best size isn't on hand.

A thread gauge calculator also tells you what a ring or plug gauge should do. Under ASME B1.2, a GO gauge must thread on fully by hand, and a NOT GO gauge may take up to 3 turns. ISO 1502 allows the NOT GO no more than 2 turns.

How to Use a Thread Calculator on an Unknown Thread

To identify a thread, measure the outside diameter across the crests with calipers. Then measure the pitch with a thread gauge, or count the crests over 1 in or 25 mm.

Enter both readings in a thread calculator and compare them to the nearest standard size. A worn or plated bolt reads slightly under nominal, so a 0.245 in reading with 20 crests per inch is a 1/4-20 UNC, not an odd size.

Pitch decides the match more than diameter. Several inch and metric threads are close in size but differ in pitch, and the wrong nut will start, then bind after a few turns.

For imperial to metric threads, a thread calculator in inches or millimeters converts the pitch first. One millimeter of pitch equals 25.4 TPI, so M8 × 1.25 is 20.3 TPI and 5/16-18 is a 1.41 mm pitch.

A thread that matches nothing may be a pipe or power thread. A pipe thread calculator needs the taper as well as the pitch, and NPT tapers 1:16 on diameter, which the Taper Calculator handles.

Trapezoidal and ACME threads use 30° and 29° profiles, so a trapezoidal thread calculator needs different factors than the 60° ones here.

Stress Area and Thread Strength

A bolt breaks at its threads, so its strength uses the tensile stress area, not the shank area. A thread sizes calculator works it out from the mean of the pitch and minor diameters.

$$A_s=\frac{\pi }{4}{\left(D-0.9743\times P\right)}^2$$

That is the UN form with D and P in inches. ISO metric threads use 0.938194 in place of 0.9743. A 1/4-20 has 0.0318 in² of stress area, and an M10 × 1.5 has 58.0 mm².

Multiply the stress area by the proof stress to get the proof load. SAE J429 Grade 5 runs 85,000 psi from 1/4 to 1 in and 74,000 psi over 1 in to 1-1/2 in, as the American Fastener grade chart lists.

A 1/4-20 Grade 5 bolt therefore holds about 0.0318 × 85,000 = 2,700 lbf at proof. An M10 class 8.8 bolt, at 580 MPa proof stress, holds 58.0 × 580 = 33.6 kN.

The Bolt Area Calculator covers stress area alone. For tightening, the Bolt Preload Calculator and Bolt Torque Calculator take it from there.

How to Calculate Thread Length on a Bolt

Thread length can mean two things. One is how much of a bolt is threaded, the other is how deep a thread must engage. A thread calculator answers the second through the minimum engagement above.

For the threaded length of hex cap screws, ASME B18.2.1 uses twice the diameter plus 1/4 in for lengths up to 6 in. ISO 4014 bolts use 2d + 6 mm for lengths up to 125 mm, so an M10 × 80 bolt has 26 mm of thread.

Fastener length itself depends on the grip and the nut. The Bolt Length Calculator and Screw Length Calculator work that out from material thickness.