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Cuts

Trapezoid Calculator

Taper angle, cut length and area for a tapered piece.

Your measurementsEvery assumption editable01

The shorter parallel side.

The longer parallel side.

Perpendicular distance between the two parallel sides.

Taper and cutCalculated live02

Result

7.59° taper

Set the saw to 7.59° — leg 30.265 in

Parallel sides
12 and 20 in
Height
30 in
Offset per sloped sidehalf the width difference each side
4 in
Sloped side lengththe actual cut length
30.2655 in
Taper from verticalthe angle to set off square
7.595°
Included angle at the base
97.595°
Taper per footfor setting a taper jig
1.6 in/ft
Area3.3333 sq ft
480 sq in

Two angles get quoted for the same cut and they are complements of each other. The taper from vertical is what you set off square — on most mitre saws and taper jigs that is the number. The included angle at the base is what a protractor reads against the long side. Confirm which one your tool wants before cutting.

The sloped side length is the real cut length, and it is always longer than the height. On a steep taper that difference is substantial, so stock cut to the height figure will come up short.

Set a right trapezoid when all the taper falls on one side — a raking cut against a wall, or a single tapered leg. The isosceles setting splits the difference across both sides, which is the usual case for a tapered post, hopper or planter.

Enter the two parallel sides and the height, and this gives the angle to set, the true length of the sloped cut, and the taper per foot for a jig. Choose whether the taper splits across both sides or falls entirely on one.

Why use this tool?What it does differently03

Why use this tool?

The angle to actually set

Taper from vertical, which is what a mitre saw and a taper jig are set from — with the complementary base angle alongside.

True cut length

The sloped side is always longer than the height. Stock cut to the height figure comes up short.

One side or both

Isosceles for a tapered post or hopper, right trapezoid for a raking cut against a wall.

Taper per foot

The figure a taper jig is normally set by, rather than an angle.

How this worksThe method04

How this trapezoid calculator works

The width difference between the two parallel sides is the total offset. Split across both sides it halves; on a right trapezoid it all falls on one. That offset and the height form a right triangle, and everything else follows from it.

The sloped side is that triangle's hypotenuse, so it is always longer than the height — the steeper the taper, the greater the difference. Cutting stock to the height figure is a reliable way to come up short.

Area is the average of the two parallel sides times the height, which holds whether the taper is symmetrical or not. Where the slope sits changes the angles but never the area.

How to use itStep by step05

How to use it

  1. Step 1: Measure both parallel sides

    Top and bottom widths — the two sides that do not slope.

  2. Step 2: Measure the height

    Perpendicular between them, not along the slope.

  3. Step 3: Choose the taper

    Both sides equally, or all of it on one.

  4. Step 4: Check which angle your tool wants

    Taper from vertical for a saw set off square; the base angle for a protractor against the long side.

Example usageWorked figures06

Example usage

A tapered planter side
12 in top, 20 in bottom, 30 in high, tapered both sides: 4 in offset per side, a 7.59° taper, and a 30.27 in sloped cut. Area is 480 sq in.
A raking cut against a wall
The same dimensions as a right trapezoid put all 8 in of offset on one side — a 14.93° taper and a 31.05 in cut. Same area, very different angle.
A gentle furniture taper
A leg 2 in at the top, 2.5 in at the bottom over 28 in gives just 0.51° per side, or 0.107 in per foot — the sort of taper a jig is set for rather than a saw angle.
Frequently asked questionsCommon questions07

Frequently asked questions

How do I find the angle for a tapered cut?

Take the offset on one sloped side and the height, and the taper from vertical is the arctangent of offset over height. That is the figure you set off square on a saw.

Why are two different angles given?

They are complements of the same cut. The taper from vertical is measured off square, which is how saws and taper jigs are set. The included base angle is what a protractor reads against the long parallel side.

How long does my stock need to be?

At least the sloped side length, not the height. On a steep taper the sloped side is noticeably longer, and cutting to the height figure leaves the piece short.

What is the difference between isosceles and right?

Isosceles splits the taper evenly across both sides — a tapered post, hopper or planter. A right trapezoid keeps one side square and puts all the taper on the other, which suits a raking cut against a wall.

How do I calculate trapezoid area?

Average the two parallel sides and multiply by the height. Where the slope falls does not affect the area, only the angles.

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