Calculate ovals
There are several methods for constructing ovals. We will show you how to calculate ovals precisely and how to realise them graphically.
Determine the proportions
Here you can see the oval construction. You can construct ovals from 3, 4, 5... circles and change the proportions in the process.
Here too, there are formulae to determine the correct dimensions.
Formulas for oval calculation:
You can now reach for your pocket calculator or use our practical online calculator.
| Ovals from | 3 | 4 | 5 | circles | |
| Oval length given | Radius(r) = | oval length/4 | oval length/5 | Oval length/6 | |
| Oval width given | Radius(r) = | Oval width/ (6-0.866*4) | Oval width/ (8-0.866*6) | Oval width/ (10-0.866*8) | |
| Calculate circumference | u = | 10/3*r*π | 12/3*r*π | 14/3*r*π | |
| Calculate radius(R) | Radius(R) = | 3*r | 4*r | 5*r |
If, for example, we want to design an oval with a fixed width or a fixed length, we simply select the formula developed for this.
An example: We want to design a table top in the shape of an oval with a width of 120 cm. We consider the oval constructed from 3 circles.
Here is the calculation:
r = oval width / (6-0.866*4)
r = 120 cm / (6-0.866*4)
r = 47.32 cm
r = 473 mm
The next step is to construct. Our sketches show you how to construct.
The geometric construction - explained step by step
1. determine the dimensions
Firstly, we need three circles with a calculated radius. The centre of the outer circles lies at the intersection of the central axis with the circle drawn first. You can use a home-made compass consisting of a wooden or plastic strip in which you drill a hole for the pencil. For really precise work, we recommend compass heads, for example our Veritas bar compass heads or the Kunz compass heads. You will also find rulers and squares in our programme.
2. determine the intersection points
Next, starting from the centre line of the middle circle, draw lines upwards and downwards at a 60° angle. Together with the centre line, these lines form equilateral triangles.
3. draw oval sides
The intersection points of these triangles are taken as the centres for the next circles. The radius can either be calculated or, if it has to be done quickly and not exactly, simply taken.
4 The oval is finished
