Thread Calculator
ConstructionCalculate the pitch diameter and minor diameter of a screw thread from major diameter and threads per inch. Free tool for machinists and toolmakers.
Reviewed by the thecalcu.com team · Last updated July 2, 2026
Minor Diameter
What is a Thread?
A Thread Calculator computes the key working dimensions of a screw thread, pitch diameter and minor diameter, from just its major diameter and threads per inch (TPI). Where a single-purpose pitch diameter tool stops at one dimension, this calculator gives a fuller picture of the thread's geometry, covering both the fit dimension (pitch diameter) and the root dimension (minor diameter) in a single pass.
Screw threads are defined by three key diameters: major diameter (the outer crest-to-crest measurement), pitch diameter (the mid-flank measurement that governs fit), and minor diameter (the inner root-to-root measurement that governs strength and tap sizing). This calculator uses the standard 60-degree thread form relationships to derive the latter two from the major diameter and TPI you provide.
If you specifically need only the pitch diameter and want a narrower, more focused tool, use the Pitch Diameter Calculator instead.
Why Use a Thread Calculator?
Whenever you're specifying, cutting, or inspecting a screw thread, you often need more than one dimension at once. A machinist selecting a tap needs the minor diameter to reference against a tap drill chart; the same machinist checking the fit of a mating nut needs the pitch diameter. Rather than running two separate calculations, this tool returns both from the same two inputs.
This is particularly useful for one-off or custom thread work, cutting a non-standard thread on a lathe, verifying a thread on an older or foreign-made part where a size chart isn't handy, or double-checking a CAD model's thread callout before it goes to the shop floor.
For torque and clamp-load calculations on the fastener once it's threaded, see the Bolt Torque Calculator. To size the clearance hole a bolt of this diameter will pass through, use the Clearance Hole Calculator.
Who Should Use This Calculator?
Machinists cutting custom threads on a lathe can use both outputs together, pitch diameter to dial in the thread-cutting tool for correct fit, and minor diameter to verify the finished root depth.
Toolmakers and die designers sizing tap drills or thread-rolling dies need the minor diameter as a starting reference point before applying standard thread-engagement allowances.
Mechanical engineering students studying fastener design can use the calculator to see how a single thread callout (major diameter and TPI) expands into a full set of governing dimensions, reinforcing the geometry behind thread standards like ASME B1.1.
Quality control technicians inspecting incoming threaded hardware can use the calculator as a fast reference check against thread gauge or optical comparator readings.
What Insights Does the Thread Calculator Give You?
Minor Diameter (in) is the headline result, the smallest diameter of the thread, measured at the root of an external thread. This dimension determines the core cross-sectional area of a bolt, which is the primary factor in its tensile strength, and it's the reference point used when selecting a tap drill size for a matching internal thread.
Pitch Diameter (in) is the secondary output, the mid-flank diameter that governs how tightly or loosely an external and internal thread mate. For a 1/4-20 thread, pitch diameter works out to approximately 0.2175 inches while minor diameter works out to approximately 0.1850 inches, illustrating how much smaller the root diameter is than the fit diameter for a coarse thread.
Viewing both dimensions together makes it easy to see the full taper of material removed by threading, from the full major diameter down to the narrow root.
How to use this Thread calculator
Enter the Major Diameter in inches, the nominal outside diameter of the thread, such as 0.25 in for a 1/4-inch fastener.
Enter the Threads Per Inch (TPI) for the thread, such as 20 for a 1/4-20 UNC thread or 28 for a 1/4-28 UNF thread.
Read the Minor Diameter in the highlighted result card, this is the root diameter of the thread, useful for tap drill selection and strength calculations.
Check the Pitch Diameter shown beneath the headline result, this is the fit-governing dimension used for thread-tolerance classes.
Cross-reference a tap drill chart if you're selecting a drill bit to tap this thread, practical tap drills are sized slightly larger than the theoretical minor diameter shown here to leave a workable percentage of thread engagement.
Show formula & methodology ↓Show less ↑
Formula & Methodology
The calculator uses the standard theoretical relationships for a 60-degree (Unified/ISO-style) thread form: Step 1, Thread Pitch: > p = 1 ÷ TPI Step 2, Pitch Diameter: > PD = D − 0.64952 × p Step 3, Minor Diameter: > MD = D − 1.29904 × p Where: - p = thread pitch in inches - D = major diameter in inches - PD = pitch diameter in inches - MD = minor diameter in inches - 0.64952 and 1.29904 = standard 60-degree thread form constants (the second is exactly double the first, reflecting the full crest-to-root depth versus the half-depth crest-to-pitch-line measurement) Worked example, 1/4-20 thread: - p = 1 ÷ 20 = 0.05 in - PD = 0.25 − (0.64952 × 0.05) = 0.2175 in - MD = 0.25 − (1.29904 × 0.05) = 0.1850 in These theoretical values align with published dimensions for a 1/4-20 UNC thread found in ASME B1.1 reference tables. If you only need the pitch diameter figure, the narrower Pitch Diameter Calculator provides the same result with a more focused single-purpose interface.
Frequently Asked Questions