KerfCalc

Splayed Side & Hopper Angle Calculator

Tilt the sides of a box outwards and both saw settings change at once. A four-sided planter with 10 degrees of splay is not cut at 45 degrees — it needs 44.4 miter and 9.85 bevel, and guessing gets you gaps.

Units

Box

0 gives an ordinary square box

Sizes

Notes

Why both settings change

Once a side leans, the joint line is no longer square to the table, so the miter closes slightly and the blade has to tilt. The two effects are linked: more splay means less miter and more bevel.

The formulas

With S the splay from vertical and N the number of sides: miter equals atan(cos(S) times tan(180/N)), and bevel equals asin(sin(S) times cos(180/N)). Both are shown in the results so you can check them.

Measuring splay

Splay is measured from vertical, not from the table. A side leaning out by 10 degrees from plumb has a splay of 10. Getting this backwards gives you a box that tapers the wrong way.

What this does not do

It gives the two saw settings. It does not size the pieces — splayed sides are trapezoids whose top and bottom widths depend on the height, and that is a separate layout.