Math formulas

Here you will learn about math formulas, including what math formulas are and how to use them.

Students will first learn about math formulas as part of measurement and data in 4th grade and 5th grade, and expand on that knowledge in geometry in 6th, 7th, and 8th grade.

What are math formulas?

Math formulas are rules that connect two or more variables. They are used to work out the values of unknown variables by substituting in other known values.

For example, here is a rectangle with base b and height h.

The formula for the perimeter P of a rectangle is:

P=2 \, (b+h)

We can use this formula to find the value of the perimeter by substituting in the values for the length and width of the rectangle.

List of math formulas

These are some of the measurement and geometry formulas you are most likely to encounter in grades 4-8.

Area \hspace{1.9cm}

Area of a rectangle	A=b \times h	Where A is area, b is the base and h is the height.
Area of a square	A=s \times s	Where A is area and s is side.
Area of a triangle	A=\cfrac{1}{2} \, b h	Where A is area, b is base and h is height.
Area of a parallelogram	A=b \times h	Where A is area, b is base and h is height.
Area of a circle	A=\pi \times r^2	Where A is area and r is radius.
Area of a trapezoid	A=\cfrac{1}{2} \, \left(b_1+b_2\right) h	Where A is area, b_1 is base 1, b_2 is base 2 and h is height.

Circumference \hspace{1.9cm}

Circumference of a circle	C=\pi d \;\; C=2 \pi r	Where C is circumference, d is diameter, r is radius.

Perimeter \hspace{1.9cm}

Perimeter of a rectangle	P=2(b+h)	Where P is perimeter, b is the base and h is the height.
Perimeter of a square	P=4 s \hspace{1.35cm} P=s+s+s+s	Where P is perimeter and s is a side.

Pythagorean Theorem \hspace{1.8cm}

Pythagorean Theorem	c^2=a^2+b^2	Where a is a side, b is a side and c is the hypotenuse.

Surface Area \hspace{1.9cm}

Surface area of a cube	A=6 s^2	Where A is area, the variable s is the side and the 6 represents the number of faces of the cube.

Volume \hspace{1.9cm}

Volume of a rectangular prism	V=b \times h \times d	Where V is the volume, b is the base, h is the height and d is the depth.
Volume of a cube	v=s \times s \times s	Where V is volume and s is side.
Volume of a cylinder	V=\pi r^2 h	Where V is volume, r is radius of the circle and h is the height.
Volume of a cone	V=\cfrac{1}{3} \, \pi r^2 h	Where V is volume, r is radius of the circle and h is the height.
Volume of a sphere	V=\cfrac{4}{3} \, \pi r^3	Where V is volume, and r is radius.

What are math formulas?

Common Core State Standards

How does this relate to 4th grade math, 5th grade math, 6th grade math, 7th grade math, and 8th grade math?

• Grade 4: Measurement and Data (4.MD.A.3)
  Apply the area and perimeter formulas for rectangles in real world and mathematical problems.

• Grade 5: Measurement and Data (5.MD.C.5b)
  Apply the formulas V = l \times w \times h and V = b \times h for rectangular prisms to find volumes of right rectangular prisms with whole number edge lengths in the context of solving real world and mathematical problems.

• Grade 6: Geometry (6.G.A.2)
  Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism.
  
  Apply the formulas V = l \times w \times h and V = b \times h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

• Grade 7: Geometry (7.G.B.4)
  Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

• Grade 8: Geometry (8.G.B.7)
  Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

• Grade 8: Geometry (8.G.C.9)
  Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

How to use math formulas

In order to solve with math formulas:

1. Use the formula given in the question.
2. Work carefully to answer the question, one step at a time.
3. Write the final answer clearly.

Math formulas examples

Example 1: perimeter of a rectangle

Find the perimeter of the given rectangle using the formula, P=2 \, (b+h).

1. Use the formula given in the question.

You will use the formula P=2 \, (b+h) to find the perimeter of the rectangle.

The length of the rectangle is 13 \, cm and the width is 5 \, cm, so substitute the measurements into the formula.

P=2 \, (13+5)

2Work carefully to answer the question, one step at a time.

P=2 \, (13+5)

Solve the operation within the parenthesis first. Adding 13 and 5 gives you 18.

P=2 \times 18

You will then multiply 2 \times 18.

This can also be solved as 18 + 18 to give the answer of 36.

P=36

3Write the final answer clearly.

The final answer is P = 36 \, cm.

The perimeter of the rectangle is 36 centimeters.

Example 2: area of a rectangle

Find the area of the rectangle given, using the formula A = b \times h.

Work carefully to answer the question, one step at a time.

A=32 \times 17

You will multiply 32 by 17.

A = 544

Example 3: area of a square

Find the area of the square given, using the formula A=s \times s.

Work carefully to answer the question, one step at a time.

A=17 \times 17

You will multiply 17 by 17.

A = 289

Example 4: volume of a rectangular prism

Find the volume of the rectangular prism using the formula, V = b \times h \times d.

Work carefully to answer the question, one step at a time.

V=9 \times 6 \times 15

First, multiply the first two numbers using the knowledge of your multiplication facts, 9 \times 6 = 54.

Multiply 54 by 15 to calculate the volume of the rectangular prism.

V=54 \times 15

V=810 \text { inches }

Example 5: area of a triangle

Find the area of the triangle given, using the formula A=\cfrac{1}{2} \, b h.

Work carefully to answer the question, one step at a time.

A=\cfrac{1}{2} \, (10 \times 15)

Following the order of operations, you will multiply 10 by 15 first.

10 \times 15=150

A=\cfrac{1}{2} \, (150)

Finally you will multiply 150 by \, \cfrac{1}{2} \, , or divide 150 by 2.

A = 75

Example 6: area of a parallelogram

Find the area of the parallelogram given, using the formula A = b \times h.

Work carefully to answer the question, one step at a time.

A=27 \times 19

To find the area, you will multiply 27 by 19.

A = 513

Teaching tips for math formulas

• Formulas can be difficult for students to memorize. Always have a way for students to refer back to the formula, such as an anchor chart or a reference sheet, until they get familiar and comfortable with each formula.

• These basic math formulas will prepare students for work in high school with more complex numbers and formulas, including linear equations, the quadratic formula, and other algebra formulas, such as the slope-intercept formula.

• While using quizzes to assess a student’s knowledge of the different equations is important, consider making the assessments real-life, and have students measure items within the classroom or school, and use the formulas to calculate the area of the classroom or playground.

Easy mistakes to make

• Substituting in the wrong number in the equation
  Learning the equation is important, but learning what each variable in an equation is equally important. In some basic math formulas, flipping the base and the height would still give students the same answer. However, as students move to more complex formulas, flipping of variables could result in incorrect answers.
  
  For example, when finding the area of a trapezoid, flipping of a side versus the height would result in the wrong answer because the sides are added together and divided by 2, and the height is not.

• Take care with writing variables clearly
  Neat writing is important. For example, the variables v and u can easily be muddled as they look similar and they both represent velocity in kinematic formulas.

Related math equations lessons

• Math equations
• One step equations
• One step equations with variables
• Solve equations with fractions
• Substitution
• Square root

The next lessons are

• Inequalities
• Types of graphs
• Number patterns
• Algebraic expressions
• Exponents

Beyond elementary

You can use formulas in lots of different areas of math. One of the most famous formulas is the quadratic formula which we can use to solve quadratic equations.

x=\cfrac{-b \pm \sqrt{b^2-4 a c}}{2 a}

Quadratics are a type of polynomial and using coordinate geometry you can use them to produce a parabola shaped quadratic graph. We can use the graph to work out the solutions to the equation and the y-intercept of the graph.

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