Drill Point Length Calculator: 118°, 135°, 140° Cone Height & CNC Z-Depth
To calculate the axial drill point cone length (h_cone) of a twist or solid carbide drill of diameter D and included point angle θ, use the right-triangle cotangent formula h_cone = (D / 2) / tan(θ / 2)—which simplifies to 0.3004 × D for 118°, 0.2071 × D for 135°, and 0.1820 × D for 140°.
Interactive Twist & Carbide Drill Point Cone Length Calculator
Compute exact conical tip length (h_cone = (D/2) × cot(θ/2)), blind-hole full-diameter Z-depth, and through-hole breakthrough Z-depth with chisel-edge margin.
How Do You Derive the 0.3004D (118°), 0.2071D (135°), and 0.1820D (140°) Cone Multipliers?
When you touch the chisel tip of a twist drill onto the top face of a workpiece to set your CNC Z-axis tool length offset (G43 Hxx), the cylindrical margins of the drill flutes sit above the workpiece surface by the vertical height of the conical drill point (h_cone). If a blueprint specifies a blind hole with a full-diameter cylindrical shoulder depth of 20.00 mm and you program G81 Z-20.0, the cylindrical bore will stop short by the entire height of the drill cone—leaving insufficient thread depth for tapping or counterboring! Under ASME Geometric & Mechanical Standards (ASME B94.11M), ISO International Metrology Standard (ISO 235), and DIN 1414 twist drill geometry, the drill point forms a symmetrical right triangle of base radius R = D / 2 and half-angle θ / 2.
Dividing the drill radius 0.5 × D by tan(θ / 2) yields the universal dimensionless cone-length constant k = 0.5 / tan(θ / 2) traceable to NIST (National Institute of Standards and Technology) and Machinery's Handbook (Industrial Press) trigonometry tables. For a conventional 118° HSS jobber drill (θ/2 = 59.0°, tan 59° = 1.66428), k = 0.5 / 1.66428 = 0.30043. For a 135° split-point cobalt drill (θ/2 = 67.5°, tan 67.5° = 2.41421), k = 0.5 / 2.41421 = 0.20711. And for a modern 140° solid carbide coolant-fed drill (θ/2 = 70.0°, tan 70° = 2.74748), k = 0.5 / 2.74748 = 0.18199—reducing bottom cone clearance by nearly 40% compared to a 118° drill!
| Drill Point Geometry (θ) | Half Angle (θ/2) | tan(θ/2) | Cone Height Formula | h for ⌀ 6.0 mm | h for ⌀ 10.0 mm | h for ⌀ 1/2 in (12.7 mm) |
|---|---|---|---|---|---|---|
| 60° Center / Spotting Drill | 30.0° | 0.57735 | 0.8660 × D | 5.20 mm (0.2047") | 8.66 mm (0.3409") | 10.99 mm (0.4330") |
| 90° NC Spot / Chamfer Drill | 45.0° | 1.00000 | 0.5000 × D | 3.00 mm (0.1181") | 5.00 mm (0.1969") | 6.35 mm (0.2500") |
| 118° Standard Jobber HSS | 59.0° | 1.66428 | 0.3004 × D | 1.80 mm (0.0710") | 3.00 mm (0.1183") | 3.82 mm (0.1502") |
| 130° Parabolic Deep-Hole HSS-E | 65.0° | 2.14451 | 0.2332 × D | 1.40 mm (0.0551") | 2.33 mm (0.0918") | 2.96 mm (0.1166") |
| 135° Heavy-Duty Split-Point Cobalt | 67.5° | 2.41421 | 0.2071 × D | 1.24 mm (0.0489") | 2.07 mm (0.0815") | 2.63 mm (0.1036") |
| 140° High-Performance Solid Carbide | 70.0° | 2.74748 | 0.1820 × D | 1.09 mm (0.0430") | 1.82 mm (0.0716") | 2.31 mm (0.0910") |
| 150° Flat-Bottom Carbide Pilot | 75.0° | 3.73205 | 0.1340 × D | 0.80 mm (0.0316") | 1.34 mm (0.0527") | 1.70 mm (0.0670") |
Why Must You Add a Breakthrough Allowance Beyond Plate Thickness + Cone Length on Through-Holes?
When drilling a through-hole across a flat plate of thickness T_plate, programming your CNC Z-depth to exactly -(T_plate + h_cone) places the theoretical sharp outer corner of the drill flutes flush with the bottom face of the plate. However, because manufacturing tolerances on rolled plate thickness vary by ±0.015" (±0.4 mm) and the outer flute corners wear into a slight corner radius, stopping at exact mathematical breakthrough leaves a thick, work-hardened ring burr around the exit hole that breaks taps and blocks deburring tools.
| Drill Bit Size & Application | 118° Cone (0.3004D) | 135° Cone (0.2071D) | 140° Cone (0.1820D) | 0.500 in Thru Z (118°) | 0.500 in Thru Z (135°) |
|---|---|---|---|---|---|
| #7 (0.2010" / 5.11 mm — 1/4-20 Tap) | 0.0604" (1.53 mm) | 0.0416" (1.06 mm) | 0.0366" (0.93 mm) | Z -0.5904" | Z -0.5716" |
| 1/4" (0.2500" / 6.35 mm) | 0.0751" (1.91 mm) | 0.0518" (1.32 mm) | 0.0455" (1.16 mm) | Z -0.6051" | Z -0.5818" |
| Letter F (0.2570" / 6.53 mm — 5/16-18) | 0.0772" (1.96 mm) | 0.0532" (1.35 mm) | 0.0468" (1.19 mm) | Z -0.6072" | Z -0.5832" |
| 6.80 mm (0.2677" — M8×1.25 Tap) | 0.0804" (2.04 mm) | 0.0554" (1.41 mm) | 0.0487" (1.24 mm) | Z -0.6104" | Z -0.5854" |
| 3/8" (0.3750" / 9.53 mm) | 0.1127" (2.86 mm) | 0.0777" (1.97 mm) | 0.0682" (1.73 mm) | Z -0.6427" | Z -0.6077" |
| 27/64" (0.4219" / 10.72 mm — 1/2-13) | 0.1268" (3.22 mm) | 0.0874" (2.22 mm) | 0.0768" (1.95 mm) | Z -0.6568" | Z -0.6174" |
| 1/2" (0.5000" / 12.70 mm) | 0.1502" (3.82 mm) | 0.1036" (2.63 mm) | 0.0910" (2.31 mm) | Z -0.6802" | Z -0.6336" |
| 3/4" (0.7500" / 19.05 mm) | 0.2253" (5.72 mm) | 0.1553" (3.95 mm) | 0.1365" (3.47 mm) | Z -0.7553" | Z -0.6853" |
To guarantee clean flute exit and shear away the exit cap cleanly, always add a Breakthrough Allowance of 0.025" to 0.040" (0.6 to 1.0 mm, or 0.10 × D on micro-drills) so your programmed through-hole Z coordinate is Z_thru = -(T_plate + h_cone + 0.8 mm). As the drill point breaks through the bottom surface and axial thrust drops, reduce feed rate by 50% on large drills to prevent helical flute grabbing. Cross-check complete tap-chamfer and chip-void allowances on our Blind Hole Tap Depth Calculator, convert wire/letter drill sizes on our 4-Way Drill Bit Size Converter, set spindle speeds on our Drill Press SFM & RPM Speeds Chart, or calculate chamfer depths on our CNC Countersink Depth Calculator.
When using indexable U-drills or replaceable-tip modular carbide drills in blind holes, remember that indexable insert drills do not form a deep conical point; instead, their stepped peripheral and central trigon carbide inserts leave a nearly flat W-shaped bottom hole profile requiring only 0.06 × D to 0.10 × D of axial tip clearance allowance when programming CNC Z-axis bottoming coordinates on vertical machining centers and lathes.