Derivation Of Value Of Pi, School Maths Lab

Q: Is 22/7 the exact value of pi?

No. 22/7 equals 3.142857..., while pi is 3.14159... to five decimal places. Pi is an irrational number, so it cannot be written exactly as a fraction; 22/7 is a convenient approximation for school calculations.

Derivation of Value of Pie for School Maths Lab

Calibrated Circular Interface: Features a 14cm diameter rotating disc integrated with a specialized 50cm linear measurement base, allowing for direct empirical observation of the $C = \pi d$ relationship.

Industrial-Grade Graduation: Utilizing high-contrast, etched metric scales on impact-resistant acrylic, the apparatus ensures parallax-free readings and structural stability for repetitive student-led experiments.

$2.71

Quick Answer: Derivation of Value of Pie for School Maths Lab is an activity set for finding the value of pi (π) by experiment: students measure the circumference and diameter of circles of different sizes and divide one by the other. The listing spells the constant ‘Pie’; the number found is pi, about 3.14.

Finding Pi by Measurement

Pi is the ratio of a circle’s circumference to its diameter, and it is the same for every circle. A derivation activity lets students discover that constancy instead of being told. They measure several circles of different sizes, divide circumference by diameter for each one and record the results in a table. Whatever the size of the circle, the quotient keeps coming out a little over three.

Circumference is measured with a thread wrapped once around the edge, marked where it meets itself and then straightened along a ruler. A second method rolls a disc along a straight line on paper for exactly one turn and measures the distance travelled. The diameter is measured across the widest part of the circle, through the centre. Doing both methods on the same disc and comparing them is a good lesson in how the method affects accuracy.

No class result will be exactly 3.14159. Thread stretches, the ruler is read to the nearest millimetre and the diameter may not pass exactly through the centre. Averaging the class’s results usually brings the value close to 3.14, and working out the percentage error against the accepted value turns the activity into a first lesson on experimental error.

Applications

Measuring circumference and diameter of several circles and tabulating C ÷ d
Showing that the ratio stays the same whatever the size of the circle
Comparing the thread method with the rolling method for circumference
Calculating the class average and the percentage error against 3.1416
Introducing the formulas C = πd and C = 2πr from the measured ratio

Specifications

Item	Activity set for deriving the value of pi (listed as “Pie”)
Quantity measured	Ratio of circumference to diameter
Measuring methods	Thread wrapped round the edge, or one full roll of a disc
Topics	Circles, ratio, measurement error, circumference formula
Contents (discs or rings, thread, scale)	Confirm at enquiry

Care & Handling

Keep the circular pieces flat and away from heat; a warped disc is no longer a true circle and spoils the ratio.
Replace thread that has frayed or stretched, as it adds to measurement error.
Store the pieces together so a full range of sizes is available for the next class.

Why Choose LabEquip

Middle-school teachers introducing circumference usually want every group to measure its own circles, so they order enough sets for the class. LabEquip lists this kit in Mathematics School Lab Products beside the Circle Kit used for circle area; send your group count through the enquiry page.

Frequently Asked Questions

Why is the ratio of circumference to diameter the same for every circle?

All circles have the same shape and differ only in size. Enlarging a circle multiplies its circumference and its diameter by the same factor, so their ratio does not change. That fixed ratio is the number called pi.

How is the circumference measured in the activity?

Wrap a thread once around the edge of the circle, mark where it meets itself, then straighten it against a ruler. Alternatively, mark a point on the edge of a disc, roll it along a line for exactly one turn and measure the distance covered.

Why do students rarely get exactly 3.14?

Threads stretch, rulers are read to the nearest millimetre and a diameter may not pass exactly through the centre. These small errors change the ratio a little. Averaging many results, and calculating the percentage error, is part of the lesson.

Is 22/7 the exact value of pi?

No. 22/7 equals 3.142857…, while pi is 3.14159… to five decimal places. Pi is an irrational number, so it cannot be written exactly as a fraction; 22/7 is a convenient approximation for school calculations.

How does the activity lead to the circumference formula?

Once students have found that circumference divided by diameter is about pi, they rearrange it as circumference equals pi times diameter. Because the diameter is twice the radius, the same formula can be written as C = 2πr.

At what level is this activity used?

It is usually done in middle school when the circumference of a circle is first taught, and it also suits older students as an introduction to measurement error and averages.

Last Updated: September 2026