Trig Calculator for Machinists

Trig for machinists, made simple. Fill in any two boxes — two sides, or one side and one angle — and everything else is worked out, with the math shown.

Right triangle

Side A (in)

Side B (in)

Side C (in)

Angle A (°)

Angle B (°)

Clear the boxes

Side A (opposite)

1.1547"

Side B (adjacent) (given)

2.0000"

Side C (hypotenuse)

2.3094"

Angle A (given)

30°

Angle B

60°

How it was worked out

1. Side A = B × tan(Angle A) → 2 × tan(30°) = 1.1547 in
2. Side C = B ÷ cos(Angle A) → 2 ÷ cos(30°) = 2.3094 in
3. Angle B = 90° − Angle A → 90° − 30° = 60°

SOH-CAH-TOA — for angle A: Sin = Opposite ÷ Hypotenuse (A ÷ C) · Cos = Adjacent ÷ Hypotenuse (B ÷ C) · Tan = Opposite ÷ Adjacent (A ÷ B). The two small angles always add up to 90°.

Where it comes up in the shop

• Angled cuts and tapers: the length of the cut is side B, the drop is side A, the angle off the axis is angle A.
• Chamfers: a 45° chamfer .050" wide on the face is .050" long on the side (A = B when angle A is 45°).
• Hole positions: a hole at an angle on a circle is the hypotenuse (the radius) with the X and Y moves as sides B and A — the bolt circle calculator below does that for every hole.

Bolt circle

Equally spaced holes on a circle: X and Y of each hole from the circle's center.

Number of holes

Circle diameter (in)

Start angle (°)

Where 0° is3 o'clock (+X)12 o'clock (+Y)

Holes numberedCounter-clockwiseClockwise

Hole positions from the circle's center

Hole	Angle	X (in)	Y (in)
1	0°	2	0
2	60°	1	1.7321
3	120°	-1	1.7321
4	180°	-2	0
5	240°	-1	-1.7321
6	300°	1	-1.7321

X is + to the right and Y is + away from you (up on the print), measured from the circle's center, looking down on the part — the same as G-code on a mill with the part zero at the center. Each hole: X = r × cos(angle), Y = r × sin(angle), r = diameter ÷ 2.