# How to calculate the perimeter of an oval

Written by joan whetzel
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Ovals, or ellipses, look like horizontally elongated circles. Accurately finding the perimeter (circumference) requires some rather complicated calculus formulas. However, a much simpler formula provides a rough estimate that falls within 5 per cent of the value found by using the calculus equations. The rough estimate equation --- circumference≈2 π√1/2(a squared + b squared) -- begins with finding: (a) the semi-major axis (longer, horizontal radius) and (b) the semi-minor axis (shorter, vertical radius). The mathematical functions used in this equation include squaring and then adding the axes as well as division, square root and multiplication.

Skill level:
Moderate

• Ruler
• Oval diagram

## Instructions

1. 1

Find the oval's (a) semi-major axis by using the ruler to measure the longer, horizontal diameter, measuring from one side of the horizontal perimeter to the other, going through the centre point of the oval. For example: a = 10 feet. Make a note of the semi-major axis length on the oval diagram.

2. 2

Find the (b) semi-minor axis by using the ruler to measure the shorter, vertical diameter, measuring from one side of the vertical perimeter to the other, going through the centre point of the oval. Example: b = 6 feet. Jot down the semi-minor axis length on the oval diagram.

3. 3

Square both the semi-major and semi-minor axes and then add them together. Example: (a squared + b squared); (10 squared + 6 squared) = (100 + 36) = 136. Write down this number next to the oval diagram or on a separate piece of paper.

4. 4

Taking the value found, either multiply it by 1/2 or divide it by 2. Example 1/2(a squared + b squared); 1/2 x (100 + 36) = 1/2 x 136 or 136 / 2 = 68. Record this value.

5. 5

Using a calculator with the square root function, find the square root for the quotient, which will give a decimal value. Example: √1/2(a squared + b squared); √1/2(100+36) = √68 = 8.2462113. Write down the square root.

6. 6

For this final step, multiply 2π by the square root value. Note that this value will also contain decimals. Example: 2π√1/2(a squared + b squared); 2π√1/2 x (100 + 36) = 2π√68 = 2π x 8.2462113 = 2 x 3.14 x 8.2462113 = 51.786207. The circumference, or perimeter, of the oval is 51.786207 feet. Record the final answer inside or next to the diagram of the oval.

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