This page lists ways in which important mathematical functions and formulas can be expressed using the Scratch Operators Blocks (in alphabetical order). Note: Since pi is an irrational number, it is up to the user to decide the number of decimal places it is rounded to. 3.14 is the conventional rounding.

Conventional measurement abbreviations

Abbreviation Measurement
b Length of a side of the base
h Height
l Slant Height
A, B, C Side lengths of a triangle
a, b, c Angle measures of a triangle (angle a is opposite side A)

Common Constants

Constant Approximate Value
pi (π) 3.141592653

Area and Surface Area

Circle

((pi) * ((r) * (r)))

Cone

(((pi) * ((r) * (r))) + ((pi) * ((r) * (l))))

Sector of a Circle

This will find the answer in degrees:

(((central angle)/(360))*((pi)*((r)*(r))))

Sphere

((pi)*((4)*((r)*((r)*(r)))))

Square-based Pyramid

(((2)*((b)*(l)))+((b)*(l)))

Trapezoid/Trapezium

Here, "a" and "b" are the two parallel sides of the trapezoid.

((((a)+(b))*(h))/(2))

Triangle

There are numerous ways to calculate the area of a triangle:

2 known side lengths (a and b) and 1 known angle between the sides (C):

(((a)*(b)) * (([sin v] of (C)) * (2)))

Two known angles (A and B) and one known side length between the two angles (c):

((((c)*(c))*(([sin v] of (A))*([sin v] of (B))))  / ((-2)*([sin v] of ((A)+(B)))))

3 known side lengths (A, B, C), also called Heron's formula:

set [s v] to ((((A)+(B))+(C))/(2))//s is called the semiperimeter
set [area v] to ([sqrt v] of ((((s)*((s)-(A)))*((s)-(B)))*((s)-(C))))

Cosine Rule

For Sides

This will give an answer for side "c":

For Angles

This will give an answer for angle "C":

Cubic Formula Note: This formula may deal with complex numbers that cannot be handled by Scratch, if it were to be worked out properly, the complex numbers would cancel out, but unfortunately here a lot of problems will be unsolvable due to the nature of Scratch.

This will give the answer to the equation:

The analogous formula for this is:

In Scratch this translates to:

Sine Rule

For Sides

This will give an answer for side "a":

For Angles

This will give an answer for angle "A":

Pythagorean theorem

This will give the length of the hypotenuse:

And these will give the length of sides "a" and "b" (assuming the hypotenuse is "c"):

Distance between two points

set [a v] to (((x1)-(x2))*((x1)-(x2)))
set [b v] to (((x1)-(x2))*((x1)-(x2)))
set [dist v] to ([sqrt v] of ((a)+(b)))

These will give the two possible answers of "x":

Volume

Cylinder

((pi)*((r)*((r)*(h))))

Sphere

(((4)/(3))*((pi) * ((r)*((r)*(r)))))

Square-based Pyramid

((((b)*(b))*(h))/(3))