What angle do you cut a sloped box or hopper at?
A four-sided box with 45°-sloped sides — a hopper, a planter, a bird feeder — is cut at 35.3° miter and 30° bevel. Settings for other side counts and slopes.
A 4-sided box with its walls sloped 45.0° from horizontal is cut at 35.3° miter and 30.0° bevel.
This is the compound miter every table of settings opens with, because a square hopper at 45° is the simplest case that needs both a miter and a bevel at once.
How that is worked out
- A box with vertical sides is just a flat miter — half the corner angle, no bevel, the same arithmetic as a picture frame. Slope the walls outward or inward and the saw has to swing and tilt together, exactly the way crown molding does against a wall and ceiling.
- The two numbers depend on how many sides the box has and how far the walls lean: at 4 sides and a 45.0° slope, that works out to 35.3° / 30.0°.
- A steeper slope pushes the bevel up and the miter down. Fewer sides push both the miter and the bevel up — a many-sided octagonal planter is close to a flat miter with almost no bevel, while a steep four-sided hopper needs a lot of both.
Miter and bevel by side count and wall slope
| Sides | 15° slope | 30° slope | 45° slope | 60° slope |
|---|---|---|---|---|
| 4 | 44.0° / 10.5° | 40.9° / 20.7° | 35.3° / 30.0° | 26.6° / 37.8° |
| 5 | 35.1° / 8.8° | 32.2° / 17.1° | 27.2° / 24.6° | 20.0° / 30.6° |
| 6 | 29.1° / 7.4° | 26.6° / 14.5° | 22.2° / 20.7° | 16.1° / 25.7° |
| 8 | 21.8° / 5.7° | 19.7° / 11.0° | 16.3° / 15.7° | 11.7° / 19.4° |
Worth knowing
- Slope is measured from horizontal — 0° is a flat ring or frame (pure miter, no bevel) and 90° is a straight-sided box (pure bevel, no miter). A hopper or a planter is usually somewhere between 30° and 60°.
- This is the same geometry the segmented ring calculator uses for a turned bowl or vase, just with a small number of sides instead of a dozen or more. A square hopper is a four-sided ring.
- Cut a test corner from scrap before committing the good stock. The two settings interact, so a small error in either one shows up as a gap that is easy to misdiagnose as the wrong setting on the other axis.
- The steeper the slope, the more the joint is long-grain to long-grain and the better it glues. A shallow, nearly-flat slope leaves more end grain in the joint and wants a spline or a reinforced corner.
Work out your own numbers
- Segmented rings and columns
Miter and bevel for any number of sides, flat or flared, and how long each segment has to be.
- Crown molding angles
The miter and bevel for any corner and any spring angle, plus the single setting for cutting it nested.
- Miter angle calculator
The miter for baseboard, casing or chair rail at any corner angle — flat trim, so there's no bevel to set.
Related questions
- What angle do you cut a four-sided planter box at?
- It depends on how far the sides lean, but the classic case — walls sloped 45° from horizontal — is 35.3° miter and 30° bevel. Shallower slopes need less bevel and more miter; steeper slopes the reverse. The segmented ring calculator handles any combination of sides and slope directly.
- Is a hopper the same joint as a compound miter on crown molding?
- Geometrically, yes — both are a miter and a bevel set together because the material leans out of the flat plane the saw table defines. Crown molding is effectively a two-sided version of this joint, leaning against a wall and ceiling at a fixed spring angle. A hopper generalizes it to any number of sides and any slope.
- How many sides should a hopper or planter have?
- Four is the common choice because it is the easiest to build square and glue up, but any number works — a hexagonal or octagonal hopper looks more refined and needs a shallower miter per corner, at the cost of more joints to get right. The table above has the settings for the sides people actually build.