Expressing π to a given Number of Significant Figures Calculator

The Expressing π to a given Number of Significant Figures Calculator (Pi Sig Fig Calculator) will calculate:

1. The value of Archimedes Constant π expressed in the desired number of significant figures (maximum 1500)

Pi Sig Fig Calculator Parameters: The calculator will calculate up to 1500 significant figures

Please note that the formula for each calculation along with detailed calculations is shown further below this page. As you enter the specific factors of each pi sig fig calculation, the Pi Sig Fig Calculator will automatically calculate the results and update the formula elements with each element of the pi sig fig calculation. You can then email or print this pi sig fig calculation as required for later use.

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Theoretical description

Archimedes' Constant π is an irrational number that represents the ratio of the circumference of a circle to its diameter, i.e.

Given that the diameter of circle is d = 2R where R is the radius of circle, we obtain the formula for the circumference of a circle:

Another quantity in geometry that involves π is the area of a circle, which is given by

A more modern meaning of π consists on the value of the defined integral shown below:

This is because one may directly compute the arc length of the top half of the unit circle, given in Cartesian coordinates by the equation x² + y² = 1, as the above integral.

This special number (π) has a wide range of application in practice, from Physics to Chemistry, Astronomy, etc.

The value of π expressed in some decimal places is

Giving that π is an irrational number (you can derive this from the fact that the digits after the decimal place shown above have no regularity or repition), it cannot be expressed as a fraction. The number of digits after the decimal point expressing π is infinite; however, we limit ourselves to the number of significant figures we are interested to use.

Sometimes, approximate values of π expressed as fractions are used. For example, we often use the fraction 22/7 to express π because 22/7 = 22 ÷ 7 = 3.142857142857142, which is very close to the correct value of π. Another fraction used as an approximate value for π is 355/113 which gives 3.14159292035398 You may notice that this value is more accurate than 22/7 though it is still not 100% accurate.

You have to round the value of π to a given number of significant figures depending on the situation involved. For example, if you have a radius measured in a number of centimetres (or even metres, no matter) expressed in one digit, the result of circumference or area must be expressed in one significant figure. Hence, in such cases, we often take π ≈ 3 (we round it to the nearest unit). When the radius contains two digits (2 s.f.) we round π to the nearest tenth (π ≈ 3.1), and so on. The most common approximation for π is 3.14, but other approximations are also made.