Countersink Depth Calculator: Depth, Diameter and Plunge for 82°, 90°, 100° and 120° Countersinks
Find countersink depth from the diameter (or diameter from depth) for 60°–120° tools, with inch #2–1/2 and ISO M3–M20 flat-head screw sizes and the plunge past a pilot hole.
How it works
depth = (D ÷ 2) ÷ tan(angle ÷ 2) · D = 2 × depth × tan(angle ÷ 2) · depth below the hole edge = (D − hole) ÷ 2 ÷ tan(angle ÷ 2) · D with a recess r = head + 2 × r × tan(angle ÷ 2)
A countersink is a cone. Cut it in half and you get a right triangle whose base is half the countersink diameter D and whose angle at the point is half the tool angle, so depth = (D ÷ 2) ÷ tan(angle ÷ 2). A 90° countersink is exactly half as deep as it is wide; an 82° one is a little deeper and a 120° one much shallower. Most countersinks are cut over an existing pilot or clearance hole, so the tool tip drops into the hole and only starts cutting when its cone touches the hole edge. The calculator gives that plunge, (D − hole) ÷ 2 ÷ tan(angle ÷ 2), which is what you set on a drill-press stop or microstop cage. Pick an inch (#2 to 1/2, 82°) or metric (M3 to M20, 90°) flat-head screw and it uses the theoretical sharp head diameter from ASME B18.6.3 or ISO 10642; under More options you can sink the head below flush or check that the countersink does not eat too far into thin material. Unlike the pilot hole and tap drill calculators, which size the straight hole, this one sizes the conical seat for the head. Results are geometry only: real tools with a flat or a pilot tip, and heads made under their nominal size, change the seat slightly, so test on scrap first.
Worked example
A 1/2 in (0.500 in) countersink with an 82° tool over a 1/4 in hole: the half angle is 41° and tan 41° = 0.8693. Depth to the cone point = 0.250 ÷ 0.8693 = 0.288 in (about 9/32 in, 7.30 mm). Because the 0.250 in hole removes the tip of the cone, the tool cuts (0.500 − 0.250) ÷ 2 ÷ 0.8693 = 0.144 in after it first touches the hole edge. The chamfer is 0.125 in wide and the cone face is 0.191 in long.
Sources: Omni Calculator: Countersink depth (depth = radius ÷ tan of half angle) · Engineers Edge: Flat countersunk head machine screws, ASME B18.6.3 head diameters · Engineers Edge: ISO 10642 countersunk socket head screw dimensions (dk)
Frequently asked questions
How deep should a countersink be?
Deep enough that its diameter at the surface equals the screw head diameter, so the head sits flush. For an 82° countersink that is about 0.575 × the diameter; for 90° it is 0.5 × the diameter; for 100° about 0.42 ×; for 120° about 0.29 ×. A #10 flat-head screw (0.385 in head) needs an 82° countersink about 0.221 in deep to the cone point.
What angle countersink do I need for my screws?
US inch flat-head wood and machine screws use 82°. Metric countersunk screws (ISO 10642, ISO 7046, DIN 7991) use 90°. Aircraft rivets and many aerospace screws use 100°, and 120° is used for thin sheet and some rivets. Using the wrong angle makes the head bear only on its rim or underside.
How do I measure countersink depth with a pilot hole?
Measure the diameter at the surface rather than the depth, or zero your stop when the tool first touches the hole edge and then plunge (D − hole) ÷ 2 ÷ tan(angle ÷ 2). With a 1/4 in hole and an 82° tool, a 1/2 in countersink needs only 0.144 in of plunge after contact.
Should a countersunk screw sit flush or below the surface?
For metal parts, flush or up to a few thousandths of an inch below. In wood that will be filled or plugged, sink it deeper; enter the recess under More options and the calculator widens the countersink by 2 × recess × tan(angle ÷ 2).
What is the difference between a countersink and a counterbore?
A countersink is a cone for a flat (tapered) head. A counterbore is a flat-bottomed cylindrical recess for a socket-head cap screw or a plug. Counterbore depth is simply the head height plus any recess, so it needs no trigonometry.
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This calculator is for educational purposes. Double-check important results before acting on them.