How Do You Calculate Pi?

Pi is an irrational number — a number with an unending string of non-repeating digits after the decimal point. While it has been calculated to more than 10 trillion places, most of the time just a few decimal places will do. We'll look at two different ways to calculate pi: By measuring a circle and by solving a mathematical equation.

Step 1

An easy way to estimate the value of pi is to divide a circle's circumference by its diameter. Measure the circumference of a cylinder or circle using a thin piece of string. (The circumference is the distance around the circle.)

Try to match the edge of the circle to the string as best as you can; the more closely your string matches the circle's circumference, the more accurate your measurement of pi will be. Mark or cut the string, and use a ruler to measure the string's length.

Step 2

Measure the diameter of the circle with your ruler. Make certain the ruler goes through the center of the circle, as a small error here can lead to a big error in the calculation.

Step 3

Divide the circumference you found in Step 1 by the diameter you found in Step 2. For example, if your circumference from Step 1 is 44 centimeters, and your diameter is 14 cm, then 44/14=3.14.

Step 1

Pi can be estimated using many methods, including complex formulas such as Leibniz's formula. This is what it looks like.

Step 2

As with all formulas to calculate pi, any number is just an estimate and the calculation goes on forever — the more you do it, the more accurate the result generally becomes.

Step 3

To try your hand at Leibniz, calculate just the first 3 terms, like this:

1 – (1/3) + (1/5)

That's 1 – .333 + .200 = .867

Multiply that by 4, and you get an approximate pi value of 3.47.