Formulas & sources
SpindleMate shows the formula and the substituted values behind every result. This page lists all formulas and where the reference data comes from, so you can check them yourself.
Internal units: length mm, cutting speed m/min, spindle speed min⁻¹ (rpm), feed mm/rev, mm/tooth or mm/min, power kW, mass kg. Inch values are converted at input and output only.
Lines marked ≈ are common shop approximations. Tool makers use slightly different coefficients; the app states which one it uses.
Cutting speed and spindle speed
Vc = π · D · n / 1000 [m/min]n = 1000 · Vc / (π · D) [min⁻¹]SFM = π · D[in] · n / 12n_used = min(n, n_max); Vc_actual = π · D · n_used / 1000
Turning
Vf = f · n [mm/min]Tc = L · i / Vf [min]Pc = ap · f · Vc · kc / (60 · 10³ · η) [kW]Rz ≈ f² / (8 · rε) · 1000 [µm]≈Ra ≈ f² / (18√3 · rε) · 1000 ≈ 32 · f² / rε [µm]≈f_max = √(8 · rε · Rz / 1000)
Milling
Vf = fz · z · n [mm/min]Q = ap · ae · Vf / 1000 [cm³/min]Pc = ap · ae · Vf · kc / (60 · 10⁶ · η) [kW]
Drilling
Vf = f · n [mm/min]Lp = (D / 2) / tan(σ / 2) (σ = 118° → Lp ≈ 0.30 · D)Tc = (L + Lp) / Vf [min]Pc = f · Vc · D · kc / (240 · 10³ · η) [kW]≈countersink depth = (D_cs − d_pilot) / (2 · tan(θ / 2))
Specific cutting force and power
kc = kc1 · h^(−mc) [N/mm²]turning: h = f · sin κr; milling: h ≈ fz≈HP = kW / 0.7457; η = 0.8 (default)
Tapping and tap drills
cutting tap (metric): d = D − Pthread % (metric) = 76.98 · (D − d) / Pthread % (inch) = TPI · (D − d) / 0.01299≈forming tap: d = D − 0.0068 · % / TPI (inch); d = D − 0.0068 · % · P (metric)≈Vf = P · n; G95: F = P; inch: F = 1 / TPI
Threads (ISO 68-1 basic profile)
H = 0.866025 · Pd2 = d − 0.649519 · PD1 = d − 1.082532 · Pd3 = d − 1.226869 · PUN: P = 1 / TPIthread depth (radius): external h3 = 0.61343 · P; internal H1 = 0.54127 · P≈infeed (constant chip area): depth after pass i = a · √(i / N)lead angle φ = atan(P · starts / (π · d2))
Parting and grooving cycle time
D_lim = 1000 · Vc / (π · n_max)t1 = π · (Ds² − max(De, D_lim)²) / (4000 · Vc · f) (CSS zone, D ≥ D_lim)t2 = (min(Ds, D_lim) − De) / (2 · f · n_max) (rpm-limited zone)t = t1 + t2
Tool nose radius compensation
offset the programmed contour by rε; P_tip = P_center + rε · (s_x, s_z), (s_x, s_z) ∈ {−1, 0, +1} from tip direction T1–T9line at angle θ to Z: ΔZ = rε · (1 − tan(θ / 2)), ΔX(radius) = rε · (1 − tan((90° − θ) / 2))arc: convex R + rε, concave R − rε (R ≤ rε cannot be machined)
Taper, bolt circle, true position
α = atan((D − d) / (2 · L)); taper = 1 : L / (D − d); TPF = 12 · (D − d) / Lx_i = cx + (PCD / 2) · cos(θ0 + i · 360° / n); y_i = cy + (PCD / 2) · sin(θ0 + i · 360° / n)chord = PCD · sin(180° / n)Ø TP = 2 · √(Δx² + Δy²)
Material weight
round bar V = π / 4 · D² · L; tube V = π / 4 · (D² − d²) · Lsquare V = a² · L; hexagon (across flats s) V = (√3 / 2) · s² · L; flat V = b · t · Lm = V · ρ · 10⁻⁶ [kg] (V in mm³, ρ in g/cm³)
Symbols
| Symbol | Meaning |
|---|---|
Vc | Cutting speed |
n | Spindle speed |
D, d | Diameter |
f | Feed per revolution |
fz | Feed per tooth |
z | Number of teeth / flutes |
Vf | Feed rate |
ap, ae | Depth of cut, width of cut |
kc, kc1, mc | Specific cutting force and its material constants |
η | Machine efficiency |
rε | Nose radius |
P, TPI | Pitch, threads per inch |
Tc, Pc, Q | Cutting time, cutting power, metal removal rate |
Sources of reference data
- ISO 68-1 — ISO general purpose screw threads: basic profile
- ISO 261 / ISO 262 — metric screw threads: general plan, selected sizes
- ISO 965-1 / ISO 965-2 — metric screw threads: tolerances
- ASME B1.1 — Unified inch screw threads (UN, UNR)
- ASME B1.20.1 — Pipe threads, general purpose, inch (NPT)
- ISO 7-1 — Pipe threads where pressure-tight joints are made on the threads (R, Rc, Rp)
- ISO 228-1 — Pipe threads where pressure-tight joints are not made on the threads (G)
- ISO 286-1 / ISO 286-2 — ISO code system for tolerances on linear sizes
- ASTM E140 / ISO 18265 — Hardness conversion
- Tool manufacturers’ published technical formulas (turning, milling, drilling power)
Values that can be derived from a standard’s formulas are calculated, not copied. Table values contain numbers only, not the text of the standards. The current edition of each standard prevails. Material grade equivalents are approximate: chemistry and properties are not identical.