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PI

Returns the mathematical constant π (pi) with 15 decimal places of precision.

Quick Example​

=PI()

Returns 3.141592653589793.

Syntax​

=PI()

Arguments​

PI takes no arguments.

Examples​

Get Pi Value​

=PI()

Returns 3.141592653589793

Calculate Circle Area​

=PI() * Radius^2

Area of circle with given radius

Calculate Circle Circumference​

=2 * PI() * Radius

Circumference of circle

Sphere Volume​

=4/3 * PI() * Radius^3

Volume of a sphere

Radians to Degrees​

=Angle_in_Radians * 180 / PI()

Convert radians to degrees

Degrees to Radians​

=Angle_in_Degrees * PI() / 180

Convert degrees to radians

How It Works​

Mathematical Constant​

PI returns the value of π (pi):

  • Ratio of circle's circumference to its diameter
  • Approximately 3.14159...
  • Irrational number (infinite non-repeating decimals)

Precision​

Sum Buddy returns PI with full double-precision:

  • Value: 3.141592653589793
  • Precision: 15-16 significant digits
  • Uses C++ M_PI constant

No Arguments Required​

PI is a constant, so it needs no inputs:

=PI()  // Correct
=PI(2)  // Error - takes no arguments

Common Use Cases​

Circle Area​

=PI() * A1^2

Where A1 is the radius

Circle Circumference​

=2 * PI() * A1

Where A1 is the radius

Cylinder Volume​

=PI() * Radius^2 * Height

Volume of a cylinder

Sphere Surface Area​

=4 * PI() * Radius^2

Surface area of a sphere

Angular Calculations​

=SIN(Angle * PI() / 180)

Calculate sine of angle in degrees

Wave Calculations​

=SIN(2 * PI() * Frequency * Time)

Sinusoidal wave function

Error Handling​

Argument Error​

If you provide any arguments, PI returns an error:

=PI(5)

Returns #VALUE! (PI takes no arguments)

Common Errors​

ErrorCauseSolution
#VALUE!Arguments providedUse =PI() with no arguments
#NAME?Function name misspelledCheck spelling: =PI not =PIE

Technical Details​

Implementation Notes​

  • Takes exactly 0 arguments
  • Returns the constant M_PI from C++ math library
  • Value: 3.141592653589793
  • Does not recalculate (constant value)
  • Not a volatile function

Precision Details​

PI in Sum Buddy:

3.141592653589793

Actual π (first 50 digits):

3.14159265358979323846264338327950288419716939937510...

The function provides sufficient precision for virtually all practical calculations.

Mathematical Applications​

Trigonometry​

=SIN(30 * PI() / 180)

Sine of 30 degrees (convert to radians first)

Geometry​

=PI() * Diameter / 2

Calculate radius from diameter, then use in formulas

Physics​

=2 * PI() * SQRT(Length / Gravity)

Period of a pendulum

Engineering​

=PI() * (Outer_Diameter^2 - Inner_Diameter^2) / 4

Cross-sectional area of a pipe

Advanced Examples​

Circle Sector Area​

=PI() * Radius^2 * (Angle / 360)

Area of circle sector with given angle in degrees

Ellipse Area​

=PI() * Semi_Major_Axis * Semi_Minor_Axis

Area of an ellipse

Arc Length​

=2 * PI() * Radius * (Angle / 360)

Length of circular arc

Torus Volume​

=2 * PI()^2 * Major_Radius * Minor_Radius^2

Volume of a torus (donut shape)

Comparison: PI vs Manual Entry​

Using PI Function​

=PI() * 5^2

Returns 78.53981633974483 (accurate)

Manual Entry​

=3.14 * 5^2

Returns 78.5 (less accurate)

Why Use PI()​

  • More accurate (15 digits vs 2-3 digits)
  • Self-documenting code
  • No risk of typos
  • Consistent across all formulas

Common Formulas with PI​

Circle Measurements​

MeasurementFormula
Area=PI() * Radius^2
Circumference=2 * PI() * Radius
Diameter=Circumference / PI()

Sphere Measurements​

MeasurementFormula
Volume=(4/3) * PI() * Radius^3
Surface Area=4 * PI() * Radius^2

Angular Conversions​

ConversionFormula
Degrees to Radians=Degrees * PI() / 180
Radians to Degrees=Radians * 180 / PI()