Miter Angle Calculator

1. Enter the corner angle in degrees. A standard inside corner is 90 degrees. For a hexagonal frame, use 120 degrees.
2. Enter the width of board A and board B. Use the same unit for both (inches, centimeters or millimeters).
3. If both boards are the same width, the calculator uses the simple half-angle formula. If they differ, it uses the arctangent formula for unequal widths.
4. Read the miter angle for each board and the matching saw setting.

Here is what each result line means:

For compound miters (crown molding with a tilt), see the compound miter calculator.

A miter angle is the angle at which a board is crosscut so that two pieces meet flush at a corner joint. The most common miter is 45 degrees, which forms a 90-degree corner when two equal-width boards are joined.

Miter joints appear in picture frames, baseboards, crown molding, door casings, deck railings and any project where two pieces of trim meet at an angle. The miter angle depends on the corner angle and, when the boards differ in width, on both board widths.

The calculator uses two formulas depending on whether the boards are the same width or different widths.

Equal-width Boards

When both boards are the same width, each board is cut at exactly half the corner angle. The saw setting is 90 degrees minus that half angle.

Unequal-width Boards

In these formulas, n is the narrower board width, m is the wider board width, and theta is the corner angle. The narrower board gets the smaller miter angle (alpha) and the wider board gets the larger angle (beta). The saw setting for each board is the absolute value of 90 degrees minus the miter angle.

1. Convert the corner angle to radians for the trigonometric functions.
2. Compute alpha using the arctangent formula.
3. Subtract alpha from the corner angle to get beta.
4. Calculate the saw setting for each board as |90 – miter angle|.

Two boards, 10 cm wide and 15 cm wide, meet at a 120-degree corner.

Step 1. The boards are unequal, so n = 10, m = 15, theta = 120 degrees.

Step 2. Numerator = 10 x sin(120) = 10 x 0.866 = 8.66.

Step 3. Denominator = 15 + 10 x cos(120) = 15 + 10 x (-0.5) = 10.

Step 4. alpha = arctan(8.66 / 10) = arctan(0.866) = 40.9 degrees.

Step 5. beta = 120 – 40.9 = 79.1 degrees.

Step 6. Saw setting for alpha: |90 – 40.9| = 49.1 degrees. Saw setting for beta: |90 – 79.1| = 10.9 degrees.

Cut the 10 cm board at 40.9 degrees (saw at 49.1) and the 15 cm board at 79.1 degrees (saw at 10.9).

Corner Angle

The corner angle is the single biggest factor. A 90-degree corner needs 45-degree miters for equal boards, while a 120-degree hexagonal corner needs 60-degree miters. Measure the actual corner angle with a digital protractor rather than assuming it is exactly 90 degrees, because walls in older buildings can be off by several degrees.

Board Width Difference

When both boards are the same width, each gets an identical cut at half the corner angle. When they differ, the narrower board receives a smaller miter angle and the wider board a larger one. The bigger the width difference, the more the two angles diverge.

Blade Kerf

A miter saw blade removes about 1/8 inch of material (the kerf). On tight-tolerance work like picture frames, account for the kerf when marking your cut line. Cut on the waste side of the line.

Material Flex and Grain

Softwoods and thin boards can flex against the saw fence, shifting the effective cut angle by a fraction of a degree. Clamp the workpiece firmly and use a stop block for repeatable cuts.

Saw Calibration

A miter saw that is not calibrated reads the wrong angle on its scale. Check it with a combination square against a known 90-degree cut before starting a project.

Regular polygons have equal interior angles. For equal-width boards, the miter angle is half the interior angle.

Interior angle of a regular polygon = (sides – 2) x 180 / sides.

Trim and Molding Corners

Baseboard, crown molding and door casing all meet at corners that may not be exactly 90 degrees. Measure the true wall angle and enter it here to get the precise miter cut.

Picture Frames

A standard rectangular frame uses 45-degree miters. Non-rectangular frames (hexagonal, octagonal, or custom angles) require the polygon formula.

Deck Railing and Fascia

Angled deck sections create non-90-degree corners at the fascia and top rail. Enter the deck corner angle to find each board cut.

Furniture and Box Joints

Jewelry boxes, planters and shadow boxes with angled sides need precise miters for tight joints.

1. Assuming the Corner Is Exactly 90 Degrees

Walls in many homes are 1 to 3 degrees off square. A 2-degree error means the miter should be 44 or 46 degrees, not 45. Measure with a digital angle finder.

2. Confusing Miter Angle and Saw Setting

Most miter saws read 0 degrees for a square (90-degree) cut. To cut a 45-degree miter, you set the saw to 45 — but for a 60-degree miter, you set it to 30 (because 90 – 60 = 30). Always convert.

3. Ignoring the Blade Kerf

The saw blade removes about 1/8 inch of material. Cut on the waste side of your mark, not centered on it, or the finished piece will be slightly short.

4. Using the Wrong Formula for Unequal Widths

The simple half-angle formula only works when both boards are the same width. If your baseboard meets a wider plinth block, you need the arctangent formula.

5. Not Making a Test Cut

Always cut a scrap piece first and check the joint before cutting your finish material. A test cut catches saw calibration errors and fence alignment problems.

The calculator uses exact trigonometric formulas and rounds results to one decimal place, which is within the precision of most miter saws (0.5 to 1 degree detent spacing).

For equal-width boards at a 90-degree corner, the miter angle is 45 degrees and the saw setting is also 45 degrees.

A regular hexagon has interior angles of 120 degrees. The miter angle for each board is 120 / 2 = 60 degrees. Set your saw to 90 – 60 = 30 degrees.

The miter angle is measured from the end of the board. The saw setting is measured from the saw fence, which reads 0 for a square cut. Saw setting = 90 minus the miter angle.

Only for flat miter cuts. Crown molding installed at a spring angle needs a compound miter (both miter and bevel). Use a compound miter calculator for that.

The calculator uses the arctangent formula: alpha = arctan(n x sin(theta) / (m + n x cos(theta))), where n is the narrower width, m is the wider width, and theta is the corner angle.

Measure the actual angle with a digital angle finder or a bevel gauge. Enter that angle instead of 90. Even 1 to 2 degrees off will produce a visible gap if you cut at 45.

Most consumer miter saws have detent stops at common angles and can be set to within 0.5 degrees between stops. For very precise work, use a digital angle gauge on the blade.

Use any consistent unit for both boards: inches, centimeters or millimeters. The miter angle depends only on the ratio of the widths, not the unit.

Many miter saws swing to 50 or even 60 degrees. For angles beyond your saw range, clamp the board at an offset angle or use a table saw with a miter gauge.

No. The calculation runs entirely in your browser and nothing you enter is stored or sent anywhere.

• OmniCalculator, Miter Angle Calculator (equal and unequal width miter formulas, worked examples, polygon angle table).
• Calculate.co.nz, Angle Cut Calculator (miter and bevel angle calculations for woodworking cuts).
• Instructables, Handy Tricks to Find Square (practical angle measurement and squaring methods for carpentry).