Circle and arc layout
Two shop tricks for drawing curves without a compass big enough to hold them: a trammel arm for a full circle, or the chord-and-rise sagitta method for a shallow arch. Print the arm itself at true size below.
Trammel arm length
12"
Diameter
24"
Circumference
75 3/8"
Trammel arm, at true size
Wider than one sheet, so it prints across 2 pieces you butt together. Print at 100%, check the ruler, then mark a batten at these two points — a nail at the pivot end, a pencil at the other.
Put a tape on the printed ruler. If it does not read exactly 6 inches, the print was scaled — set the print dialog to 100% or “Actual size” and print it again. Do not cut wood from a template that failed this.
Pivot at one end, pencil at the other. Drive a small nail through the pivot mark and swing the pencil end through the arc. For the full circle, the pivot is the circle's own center. Trim on the orange line and butt this piece to the next one — the marks either side of the join have to line up before you drill anything.
Pivot at one end, pencil at the other. Drive a small nail through the pivot mark and swing the pencil end through the arc. For the full circle, the pivot is the circle's own center. Trim on the orange line and butt this piece to the next one — the marks either side of the join have to line up before you drill anything.
Printing this properly
In the print dialog, set the scale to 100% or “Actual size” and turn off “Fit to page”. Measure the printed ruler with a tape before you trust the arm length — a radius off by a sixteenth is an arc that visibly does not close where two pieces meet.
Worked example: a 24" circle
A 24" circle is drawn with a 12" trammel arm, pivot to pencil, and runs 75 3/8" around.
The arc tab opens on a 24" chord with a 4" rise: a 20" radius, with the pivot 16" below the middle of the chord.
- Trammel arm
- 12"
- Circumference
- 75 3/8"
- Arc radius, 24" × 4"
- 20"
These are the figures the calculator above opens on. Change any field and it works the same problem for your numbers.
About laying out circles and arcs
- How do I draw a circle bigger than my compass?
- A trammel: a strip of wood with a pivot point at one end and a pencil at the radius. This gives you that radius from either a diameter or a radius you already know, so you can mark the strip once and swing the whole circle.
- What is the sagitta method for drawing an arc?
- It finds the radius of a shallow arch — a valance, a corbel, an arched rail — from two numbers you can measure directly: the chord (the straight width at the base) and the rise (how far the arc bows up at the middle). A 24" chord with a 4" rise is a 20" radius circle, which you can then strike with a trammel or a thin strip pinned at both ends and pushed to the rise.
- Why is the radius always bigger than the rise?
- The rise is only the sliver of the circle closest to the chord; the centre of that circle sits further back, behind the arc. A shallow bow — a small rise over a wide chord — comes from a very large, gentle circle, which is why architectural arches are so often drawn from a radius far bigger than the arch itself looks.
You might also need
- Grid enlargement calculatorScale a small pattern up to full size using the classic square-by-square grid method.
- Segmented rings and columnsMiter and bevel for any number of sides, flat or flared, and how long each segment has to be.
- Ellipse and elliptical archWhere the two nails go and how long the string is for the string-and-pencil method, or a table of offsets to plot the curve with a tape.