To find the center of a circle, draw two chords that are not parallel, mark the perpendicular bisector of each, and the point where the two bisectors cross is the center; on paper you can simply fold the circle in half twice and the creases cross at the center.
Every round thing has one true middle. Here is how to put your finger on it.
You need the center of a circle more often than you would think. To drill a hole in a round tabletop, hang a clock, or cut a cake into fair slices.
Guessing by eye gets you close, often within a few millimetres on a small circle. But "close" shows up fast. A cut that misses the center by 1 cm on a 20 cm cake gives one person a visibly bigger piece.
Here are five methods, from the quickest to the most exact.
This works for anything you can fold: paper circles, tortillas, tracing paper.
If the object itself cannot be folded, trace around it on paper, cut out the tracing, fold that, then lay it back on the object and poke through the crossing point.
This one feels like a trick, but it is solid geometry. Any right angle whose corner touches the edge of a circle has its two arms cross the circle at the two ends of a diameter.
The longest straight line you can fit across a circle is the diameter, and its midpoint is the center.
It is less exact than the paper corner, because the width barely changes near its maximum. Use it for a quick check, not for drilling.
This is the textbook method, and the most exact with good tools.
It works because every point on a chord's perpendicular bisector is the same distance from both ends of the chord. The only point that is the same distance from all four ends is the center.
Woodworkers use a cheap tool called a center finder: a V shape with a straight edge down the middle. Push the V against a round edge, draw a line, rotate, draw again. The lines cross at the center.
| Method | Tools needed | Accuracy | Best for |
|---|---|---|---|
| Fold twice | Paper | Good | Paper circles, tracings |
| Paper corner | Sheet of paper, pencil | Very good | Plates, lids, tabletops |
| Widest line | Ruler | Fair | Quick checks |
| Two chords | Compass, ruler | Excellent | Drawing, drafting |
| Center finder | Center finder tool | Very good | Dowels, wood turning |
A circle has a useful property: any straight cut through its center splits it into two exactly equal halves. It does not matter which direction the cut goes. Miss the center, though, and every cut is uneven.
The same holds for any shape that looks identical turned upside down, like a rectangle or an oval.
Most real objects are not like that. A cleaver has a heavy blade and a thin handle. A lantern has a wire loop on top. For shapes like these, the line that splits the area in half is rarely where the eye says the middle is.
That gap is the whole game in Halfsies. You get three hand-drawn objects a day and one cut each. A scale weighs both halves by drawn area, so a thin handle counts for little and a solid body counts for a lot. Your score for each cut is the lighter half divided by the heavier half, times 100, so a perfect day is 300. Round objects are the friendly ones. The lopsided ones are where scores drop.
Fold it in half twice at different angles. The two creases cross at the center. If you cannot fold the object, trace it on paper and fold the tracing.
Use the corner of a sheet of paper. Touch the corner to the edge of the circle, mark where the paper's edges cross the circle, and join the marks to get a diameter. Do it twice, and the diameters cross at the center.
Lay a large sheet of paper or a carpenter's square with its corner on the table edge, mark the two points where the edges cross the rim, and draw a line between them. Repeat from another spot. The lines cross at the center.
Yes. Every straight line through the center of a circle splits it into two equal halves, whatever its angle. Lines that miss the center always make one piece bigger.