Thread dimensions from the standard profiles, and spindle speeds from cutting speed
Three machining lookups, each computed from the governing standard geometry rather than a copied table. Metric ISO threads: pitch diameter, thread depths, minor diameters and the tap drill for any diameter and pitch, from the basic profile constants. Imperial UN threads: the same quantities from diameter and threads per inch, including the classic tap-drill rule. Speeds and feeds: spindle rpm from a cutting speed you choose (this page sets no cutting speeds for you, because they belong to your tool and material data) and feed rate from feed per revolution, or per tooth for milling. All thread figures are basic profile dimensions; tolerance classes shift real limits, and the content says where.
Disclaimer: This calculator gives estimates for general information only. It is not financial, medical or other professional advice. Thread fits and machining parameters for production work belong with the governing standards and your tooling suppliers’ data.
What these tools do
The thread tools expand a designation into the dimensions a machinist actually cuts and inspects to: for metric threads, the pitch diameter (the imaginary cylinder where thread and groove widths match, and the dimension fits are judged on), the external thread’s root diameter, both thread depths, and the standard tap drill; for UN threads, the pitch in millimetres, the pitch diameter and the tap drill by the long-standing rule (major diameter minus pitch), which yields about 75 percent thread engagement. The speeds tool is pure kinematics: rpm from cutting speed and diameter, feed rate from rpm and feed per revolution, and the milling variant from feed per tooth times teeth. Nothing is extrapolated across materials: the brief for this page forbids inventing cutting recommendations, so the cutting speed is your input from your data.
How to use them
- Basic dimensions are the starting line, not the gauge. A 6H internal and 6g external thread (the common commercial pairing) are offset by tolerance and allowance from these basic figures; inspection and production work uses the standard’s limit tables for the class specified on the drawing.
- Tap drill choice is an engagement trade. The standard drill gives roughly 75 percent thread, near full strength in most materials with reasonable tapping torque; hard or gummy materials are often drilled larger (lower engagement, much lower tap breakage), a workshop decision these figures inform.
- Cutting speed follows the tool maker’s data for your exact material and tool. The same geometry at the wrong speed either rubs the tool to death or burns it; this page converts your chosen speed honestly and refuses to choose it for you.
- Single-start assumed. Lead equals pitch throughout; multi-start threads (rare outside closures and special mechanisms) advance by lead, not pitch, and are outside these calculations.
The formulas
- Metric basic profile (H = 0.86603 × pitch): pitch diameter = d – 0.64952 × P; external minor (max) = d – 1.08253 × P; external thread depth = 0.61344 × P; internal thread depth = 0.54127 × P; tap drill = d – P.
- UN: pitch = 25.4 / TPI (mm); pitch diameter ≈ d – 0.64952 × pitch (in inches); tap drill = d – pitch.
- Speeds: rpm = 1,000 × Vc / (π × diameter). Feed rate = rpm × feed per rev; milling feed = rpm × feed per tooth × teeth.
Worked examples
M10 × 1.5, expanded. Pitch diameter 9.026 mm; external thread depth 0.920 mm and minor diameter 8.376 mm; internal depth 0.812 mm; tap drill 8.50 mm, the drill in every machinist’s chart, here derived rather than looked up, which is why any non-chart size (an M11 × 1.25 repair, say) is equally available.
1/4-20 UNC. Pitch 1.27 mm; tap drill = 6.35 – 1.27 = 5.08 mm, which is 0.20 inches, the Number 7 drill’s neighbourhood that imperial charts prescribe, reached by the same rule from the other unit system.
The lathe setting. A chosen cutting speed of 100 m/min on a 20 mm workpiece: rpm = 1,591.55; at 0.2 mm per revolution the feed rate is 318.31 mm/min. Two divisions stand between a catalogue cutting speed and a machine setting, and both are shown rather than hidden inside a chart’s rounding.
Reading your results
Read thread dimensions against the drawing’s tolerance class before cutting: basic figures anchor the middle of the system, and go/no-go gauges, thread wires and the standard’s limits finish the job. Read tap drill as a range decision in disguise: the printed drill is the standard compromise, and harder stock argues upward. Read rpm as a ceiling set by the tool: the machine’s available steps, workpiece balance and chuck limits may all argue lower, and finish and tool life usually improve by respecting the data the speed came from.
Limitations
- Basic profiles only. Coatings and plating build up thread flanks (a plated thread is effectively larger), special series and non-standard pitches follow their own standards, and pipe threads (tapered, sealing) are a different family entirely and are not computed here.
- No cutting recommendations. Speeds, feeds for materials, tool geometry and coolant choices live in tooling data and machining handbooks; the page implements kinematics and thread geometry only, exactly as its brief instructs.
- Engagement percentages are nominal. The tap-drill rule’s “about 75 percent” varies slightly with the exact drill chosen from the chart’s standard sizes.
- Rounding of real drills. Drills come in discrete sizes; the computed 8.50 mm exists, but a computed 7.83 mm becomes the nearest stocked drill and a slightly different engagement.
Frequently asked questions
Why is the tap drill just diameter minus pitch?
Because the internal thread’s minor diameter (the drilled hole the tap threads into) sits one full profile depth below the major diameter on each side in the basic design, and the standard simplification lands on the drill that produces roughly three-quarter engagement across both metric and UN systems. It is an approximation with a century of workshop validation, close enough that the charts machinists trust are built from it, and its limits (very coarse pitches, very hard materials) are handled by deliberately choosing a larger drill, as the guidance section notes.
What does pitch diameter actually control?
Fit and strength together: it is the dimension at which the widths of thread and space are equal, so two parts whose pitch diameters sit inside their tolerance bands assemble with the designed clearance regardless of small crest and root variations, which are deliberately cleared. That is why pitch diameter, not the eye-catching major diameter, is what thread measurement (wires, micrometers, gauges) reports, and why this page leads its results with it.
Can I use these figures for a plated or coated thread?
Not directly: plating adds material to the flanks, and a uniform coating of thickness t grows the effective pitch diameter by roughly 4t on external threads, which is why drawings specify whether dimensions apply before or after coating and why coated fasteners are produced to adjusted limits. Compute the basic geometry here, then apply the coating allowance from the applicable standard rather than discovering the interference at assembly.
Why will this page not tell me a cutting speed?
Because a responsible number needs the pairing of your exact tool (substrate, coating, geometry) with your exact workpiece material and condition, plus the machine’s rigidity and the operation type; generic tables age badly and travel worse across materials. Tool manufacturers publish tested data for those pairings, and this page’s job starts where that data is chosen: it converts the chosen speed into the machine settings without rounding them through a chart.
Related calculators
Method: ISO metric and UN basic profile constants as printed in the formula section; spindle kinematics; cutting parameters supplied by the user per the machining data rule. Last reviewed: 14 October 2026.