Ellipses in perspective
Any circle that is not square-on to you appears as an ellipse: the rims of cups, wheels, bottle tops, columns and bowls. Learn how eye level controls the shape of an ellipse, how it lines up with an object's axis, the classic mistakes, and how to construct and practise them.
Key terms
- EllipseA circle seen at an angle. It is a smooth, symmetrical oval with rounded ends, never pointed and never flat-sided.
- Major axisThe longest line across the ellipse, through its centre. It shows the true width of the circle and does not foreshorten.
- Minor axisThe shortest line across, at exactly 90° to the major axis. It is the foreshortened depth of the circle and always lies along the object's central axis.
- Ellipse degreeThe angle at which you see the circle. 0° is edge-on, a straight line; 90° is face-on, a full circle. Most everyday ellipses are between 10° and 60°.
- Eye level (horizon)A circle level with your eye is seen edge-on as a line. Horizontal circles open up the further they sit above or below it.
- Central axisThe imaginary line through the centre of a round object, such as the spindle of a cylinder or the axle of a wheel. Every ellipse on the object is built around it.
Measuring the degree: minor axis ÷ major axis = sin(degree). A 30° ellipse is half as tall as it is wide (sin 30° = 0.5); a 45° ellipse is about 0.71 as tall; a 10° ellipse only about 0.17.
Ellipses and eye level
A stack of identical horizontal circles on one vertical axis, drawn by a true perspective camera. Drag up and down on the drawing to move your eye level. The circle at eye level becomes a line; the further a circle is from eye level, the rounder (higher degree) its ellipse.
Show as
Camera
Show
A shorter viewing distance means a wider-angle view, so the degrees change faster as you move away from eye level. Move the stack sideways and the ellipses tilt slightly: a real wide-angle effect. Near the centre of the picture, keep major axes level.
Tilted axis
Tip a cylinder over and its ellipses tip with it. Whatever the angle, the minor axis of each end lies along the cylinder's central axis and the major axis crosses it at a right angle. Drag on the drawing to rotate the cylinder, or use the sliders.
Angle
Ellipse degree
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The more the axis points towards you, the rounder the ends. The far end is always a little rounder or narrower than the near one because it is seen from a slightly different angle. In strong perspective the alignment is very slightly off; in practice, draw the minor axis on the central axis.
Common mistakes
Each card shows a correct drawing on the left and the typical error on the right.
Draw it step by step
Every drawing here is a true perspective projection, so the constructions are exact. Use a pencil, draw construction lines lightly, and draw ellipses with a relaxed arm movement from the shoulder or elbow.
Guess the degree
Judge the degree of each ellipse by eye, then check. Compare the minor axis with the major axis: half as tall is 30°, about three-quarters is 50°.
Degrees
Score
Within 3° earns three stars, within 7° two, within 12° one. Press Enter in the number box to check.
Practice sheet
An A4 sheet with a reference row of ellipse degrees from 10° to 80° and rows of boxes to fill with freehand ellipses. Each box is exactly the right proportion for its degree, so a good ellipse touches the middle of all four sides.
ELLIPSE PRACTICE
Freehand ellipses: match each row's degree and touch every side of the box.
- Ghost the movement first: circle the pencil above the paper a few times from the elbow or shoulder, then lower it and draw lightly in two or three passes.
- Touch the midpoint of every side of the box. The ends must be round, not pointed, and the far half the same shape as the near half.
- Check your degree against the reference row: minor axis ÷ major axis = sin(degree).