Screw Thread Calculator
Calculate major, minor, and pitch diameters for metric and unified screw threads. Enter values for instant results with step-by-step formulas.
Reviewed by Daniel Agrici, Founder & Lead Developer
Formula
Pitch Dia = d - 0.6495p | Minor Dia = d - 1.2269p | H = p x sqrt(3)/2
Where d = major (nominal) diameter, p = thread pitch, H = fundamental triangle height. For unified threads, pitch = 1/TPI. Thread depth for external threads = 5H/8. Tensile stress area uses the mean of pitch and minor diameters.
Worked Examples
Example 1: Metric M10 x 1.5 Thread Dimensions
Problem:Calculate the pitch diameter and minor diameter for a standard M10 x 1.5 metric thread.
Solution:Major diameter (d) = 10.000 mm\nPitch (p) = 1.500 mm\nH = p x sqrt(3)/2 = 1.5 x 0.866025 = 1.2990 mm\nPitch diameter = d - 0.6495 x p = 10 - 0.6495 x 1.5 = 10 - 0.9743 = 9.026 mm\nMinor diameter = d - 1.2269 x p = 10 - 1.2269 x 1.5 = 10 - 1.8404 = 8.160 mm\nTensile stress area = (pi/4) x ((9.026 + 8.160)/2)^2 = 58.0 mm^2
Result:Pitch diameter: 9.026 mm | Minor diameter: 8.160 mm | Tensile area: 58.0 mm^2
Example 2: Unified 1/2-13 UNC Thread Dimensions
Problem:Calculate the key dimensions for a 1/2-13 UNC (Unified National Coarse) thread.
Solution:Major diameter (d) = 0.5000 in\nTPI = 13, Pitch = 1/13 = 0.07692 in\nH = 0.07692 x 0.866025 = 0.06662 in\nPitch diameter = 0.5 - 0.6495 x 0.07692 = 0.5 - 0.04997 = 0.4500 in\nMinor diameter = 0.5 - 1.2269 x 0.07692 = 0.5 - 0.09438 = 0.4056 in\nTensile stress area = (pi/4) x ((0.4500 + 0.4056)/2)^2 = 0.1419 in^2
Result:Pitch diameter: 0.4500 in | Minor diameter: 0.4056 in | Tensile area: 0.1419 in^2
Frequently Asked Questions
What are the major, minor, and pitch diameters of a screw thread?
The major diameter is the largest diameter of the thread, measured from crest to crest on an external thread or root to root on an internal thread. The minor diameter is the smallest diameter, measured from root to root on an external thread. The pitch diameter falls between the two and is the theoretical diameter where the thread width equals the space between threads. The pitch diameter is the most critical measurement for thread engagement because it determines how well mating threads fit together. Manufacturing tolerances are tightest on the pitch diameter because even small deviations affect thread strength and fit quality.
What is the difference between metric and unified thread systems?
Metric threads, designated with an M prefix, specify size by major diameter and pitch in millimeters, such as M10 x 1.5. Unified threads, used primarily in the United States, specify size by major diameter in inches and threads per inch, such as 1/2-13 UNC. Both systems use a 60-degree thread angle, making them geometrically similar but dimensionally incompatible. Metric threads are the worldwide standard for most engineering applications, while unified threads remain common in American manufacturing, aerospace, and military applications. The ISO metric system offers both coarse and fine pitch options for each diameter, with coarse pitch being the default when no pitch is specified.
How is thread pitch different from threads per inch?
Thread pitch is the distance in millimeters between adjacent thread crests, measured parallel to the thread axis. Threads per inch is the reciprocal measurement used in the unified system, counting the number of complete threads within one inch of length. The relationship is simply TPI = 25.4 / pitch(mm) or pitch = 25.4 / TPI. For example, a 1.5 mm pitch equals approximately 16.9 TPI, and 13 TPI equals approximately 1.954 mm pitch. Coarse threads have larger pitch values and fewer TPI, while fine threads have smaller pitch values and more TPI. Fine threads provide better holding power in thin materials and allow more precise adjustment.
What are thread classes and tolerance grades?
Thread classes define the fit and tolerance of threaded connections. In the metric system, tolerance grades like 6g for external and 6H for internal threads specify allowable dimensional variations. The number indicates the tolerance grade (smaller numbers mean tighter tolerances), and the letter indicates the tolerance position (lowercase for external, uppercase for internal threads). In the unified system, classes 1A, 2A, and 3A are used for external threads, and 1B, 2B, 3B for internal threads. Class 2A/2B is the most common general-purpose fit, while class 3A/3B provides a tighter fit for precision applications. Class 1A/1B allows the loosest fit, suitable for easy assembly.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy