π is the ratio of a circle’s circumference to its diameter. Measure any circle, divide the distance around by the distance across, and you get 3.14159… every time. That is why the circumference of a circle is 2πr and its area is πr², and it explains why the π key keeps turning up in geometry, trigonometry, and wave calculations.

Key Takeaways

π = circumference ÷ diameter, about 3.14159 for every circle.

π is irrational: the digits never repeat or terminate (3.141592653589793).

Area of a radius-2 circle: π × 2² = 12.5663706144.

Circumference of a radius-5 circle: 2 × π × 5 = 31.4159265359.

What π is

Pick up any circular object. Wrap a string around it, mark the length, then lay that same length across the width. The ratio of the two lengths is π, close to 3.14. The ratio does not depend on the size of the circle. A coin and a bicycle wheel both give the same value, because every circle is a scaled copy of every other circle. That scale invariance is the whole reason one number can describe them all.

The relationship is usually written two ways: circumference = π × diameter, or circumference = 2πr where r is the radius. Since the diameter is twice the radius, the two forms say the same thing.

Worked example 1: circumference from radius. A circle has radius 5. Type 2pi5 on the calculator. It returns 31.4159265359. If you would rather start from the diameter, the same result comes from pi*10.

Why the digits never end

π is irrational, which means no fraction of whole numbers equals it exactly, and its decimal expansion never settles into a repeating pattern. The calculator stores π to fifteen or sixteen digits: 3.141592653589793. Using 3.14 for rough estimates is fine, and 22/7 is a famous day to day approximation, but neither is exactly π. For precision work you keep the symbol in the expression and let the calculator apply it at the end.

The two formulas that do real work

The circumference, 2πr, and the area, πr², account for most real uses of π.

Worked example 2: area of a circle. You need the area of a circle with radius 2. Type pi*2^2. Because ^ binds tighter than multiplication, the calculator reads it correctly as π × (2²), and returns 12.5663706144. Rough check with π ≈ 3.14: 3.14 × 4 = 12.56, and the exact answer sits right next to it.

When the radius is not a whole number, say √2, the calculator still keeps π separate from the root until the final step. The calculator function reference shows how function keys like √ and the constant key π combine.

Beyond circles: volume

The same π shows up wherever circles stack into three dimensions. A cylinder of radius r and height h has volume πr²h. A sphere of radius r has volume (4/3)πr³. Neither formula has to be memorised cold if you remember that the area πr² is the base of each, and the third dimension just adds length.

Worked example: volume of a cylinder. A cylinder has radius 3 and height 5. Type pi3^25. The calculator reads it as π × 3² × 5 = 45π, and returns 141.371669412. Keep the π in the expression and the rounding happens once, at the end, instead of at every intermediate step.

π in trigonometry

Trigonometric functions take angles as input, and those angles are measured in radians or degrees. One full turn around a circle is 360 degrees, and in radians that same turn is 2π. So half a turn is π, a quarter turn is π/2, and trig identities come out cleanly in radian measure. This site defaults to degree mode, so before mixing π into a trig expression, switch to radians. The degrees vs radians guide explains the toggle and when each mode is the right one.

Worked example 3: sine of a half turn. Switch the calculator to RAD, then type sin(pi/2). It returns 1. The reason is geometric: π/2 radians is 90 degrees, and the height of the unit circle at a quarter turn is exactly 1. The trigonometry reference lists the full set of these key values.

Using the π key

Use the π key, or type pi, and the calculator keeps the constant symbolic inside the expression until you press =.
Write the whole formula before evaluating: pi*2^2 gives 12.5663706144 in one step.
π shows up in wave formulas, sin(x), cos(x), and whenever you convert degrees to radians, so a comfortable feel for where it sits saves constant rechecking.

Frequently asked questions

Is π exactly 3.14?

No. 3.14 is a rounded approximation. π is 3.141592653589793…, and the digits carry on without repeating. On the calculator, typing pi keeps the full value.

What is the value of pi?

π ≈ 3.141592653589793. The calculator stores that value internally and shows it rounded to twelve significant digits when you evaluate a bare pi.

Why does π appear in trigonometry?

Because a full circle is 2π radians, which is the same as 360 degrees. Radian angle measures are built from π, so trig identities and graphs all lean on it.

How do I type pi on the calculator?

Press the π key or type pi. It inserts the constant into your expression, so pi*2^2 evaluates as the area of the circle even though you never typed a decimal.