The formula
area = π × radius² · in wedges: perimeter ÷ width of a slice
Where it comes from
Servings come from the area, not the diameter, and that is the trap: a thirty-centimetre cake does not give twice what a fifteen gives, it gives four times. The cut changes the answer too. Small cakes are cut in wedges from the centre, and there the limit is the perimeter; big ones are cut in a grid, in rectangles, because a wedge from a forty-centimetre cake would be twenty centimetres long and impossible to eat.
How to work it out by hand
- Work out the area: pi times the radius squared
- For wedges, divide the perimeter by the width of a slice
- For a grid, divide the usable area by the area of one slice
- Compare with your guests and go up in diameter if it falls short
What is worth knowing
The standard slice for a celebration cake is about two and a half by five centimetres, which is what gets served at a wedding; for tea at home they are cut bigger, four by five. A grid loses around twenty per cent to the curved edge, and that is already taken off. If the number falls short, going up in diameter works far better than going up in height: five centimetres more across a twenty-centimetre cake gives forty per cent more servings, while a centimetre more of height gives none.