Math resources Algebra

Math formulas

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 expressions and equations in 6th grade and expand on that knowledge in high school algebra.

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.

Formulas will usually include coefficients, constants, variables, and an operator.

For example, here is a rectangle with base b and height h. . You can use a math formula to find the value of the perimeter by substituting in the values for the length and width of the rectangle.

The formula for the perimeter P of a rectangle is:

P=2 \, (b+h)

Literal equations

Literal equations are equations that have more than one variable in them. Literal equations are represented by formulas and equations.

These equations will all have more than one variable in them, and in order to solve them, you will need to isolate one of the variables. To do this, you will use the inverse operation.

Step-by-step guide: Literal equations

Kinematic equations

Kinematic equations are a set of equations that describe the motion of an object with constant acceleration. These equations can be used to predict the position, time, speed, and acceleration of an object. They are often used in precalculus, calculus, and physics classes.

The four main kinematic equations, where v_o is the initial velocity (original velocity), v is the final velocity, a is the constant acceleration, t is time, and s is the displacement (change in position). These equations can look different depending on the class you are in.  For example, displacement, which is denoted by the variable s can be denoted by x.

• Velocity-Time relation
v=v_o+a t
• Displacement-Time relation
s=v_o t+\frac{1}{2} a t^2
• Velocity-Displacement relation
v^2=v_0^2+2 a s
• Average Velocity-Displacement relation
s=\frac{\left(v_0+v\right)}{2} t

Step-by-step guide: Kinematic equations (coming soon)

List of important math formulas

The following formulas are considered important math formulas for students to know and understand, including geometry formulas.

Common Core State Standards

How does this relate to 6th grade math and high school math?

• Grade 6: Expressions and Equations (6.EE.A.2c)
Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s^3 and A = 6s^2 to find the volume and surface area of a cube with sides of length s = 1/2.

• High School: Algebra (HS.A.CED.A.4)
Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.

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

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.

Use the formula given in the question.

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

Example 3: area of a square

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

Use the formula given in the question.

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

Example 4: volume of a rectangular prism

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

Use the formula given in the question.

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

Example 5: area of a triangle

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

Use the formula given in the question.

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

Example 6: area of a parallelogram

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

Use the formula given in the question.

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

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.

• Not clearly writing variables
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.

Practice math formulas questions

1. Find the perimeter of the rectangle using the appropriate formula.

83 feet

166 feet

163 feet

85 feet

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

Substitute the values within the formula.

P=2 \, (32+51)

Add the values within the parenthesis first.

P=2 \, (83)

Then multiply 83 by 2.

The final answer is P = 166 \, ft.

The perimeter of the rectangle is 166 feet.

2. Find the area of the rectangle using the appropriate formula.

2,747 feet^2

216 feet^2

2,647 feet^2

225 feet^2

You will use the formula A = b \times h to find the area of the rectangle.

Substitute in the values within the formula.

A=41 \times 67

Multiply 41 by 67.

The final answer is A = 2,747 \, ft^2 .

The area of the rectangle is 2,747 feet^2.

3. Find the area of the square given, using the appropriate formula.

180 inches^2

1,825 inches^2

2,025 inches^2

225 inches^2

You will use the formula for finding the area of a square A=s \times s.

Substitute the value into the formula.

A=45 \times 45

You will multiply 45 by 45.

The final answer is A = 2,025 \, in^2 .

The area of the square is 2,025 inches^2.

4. Find the volume of the rectangular prism using the appropriate formula.

322 inches^3

1,510 inches^3

525 inches^3

1,610 inches^3

You will use the formula to find volume of the rectangular prism V=l \times w \times h.

Substitute the measurements into the given formula.

V=14 \times 5 \times 23

Multiply 14 \times 5, first.

Then multiply the product of 14 and 5 by 23.

The final answer is V= 1,610 \, in^3 .

The volume of the rectangular prism is 1,610 inches^3.

5. Find the area of the triangle using the appropriate formula.

988 inches^2

114 inches^2

494 inches^2

524 inches^2

You will use the formula A=\cfrac{1}{2} \, b h to find the area of the triangle.

Substitute the measurements into the formula.

A=\cfrac{1}{2} \, (38 \times 26)

Following the order of operations, multiply 38 by 26 first.

A=\cfrac{1}{2} \, (988)

Then multiply 988 by \,\cfrac{1}{2} \, , or divide 988 by 2.

The final answer is A= 494 \, in^2 .

The area of the triangle is 494 inches^2.

6. Find the area of the parallelogram using the appropriate formula.

9,408 \, cm^2.

448 \, cm^2.

623 \, cm^2.

9,308 \, cm^2.

You will use the formula A=b \times h to find the area of the triangle.

Substitute the measurements into the formula.

A=84 \times 112

You will multiply 112 and 84 together to find the area of the quadrilateral.

The final answer is A= 9,408 \, cm^2 .

The area of the parallelogram is 9,408 centimeters ^2.

Math formulas FAQs

What is the Pythagorean Theorem?

The Pythagorean Theorem states that in any right triangle, the sum of the squares of the legs equals the square of the hypotenuse. If you know the lengths of any two sides of a right triangle, you can use the Pythagorean Theorem to find the third length.

What are the six functions of trigonometry?

The six functions of an angle, used in trigonometry, are sine, cosine, tangent, cotangent, secant, and cosecant.

What is the distance formula?

The distance formula is a formula used to measure how far apart two objects or points are.

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.

Still stuck?

At Third Space Learning, we specialize in helping teachers and school leaders to provide personalized math support for more of their students through high-quality, online one-on-one math tutoring delivered by subject experts.

Each week, our tutors support thousands of students who are at risk of not meeting their grade-level expectations, and help accelerate their progress and boost their confidence.

x

[FREE] Common Core Practice Tests (3rd to 8th Grade)

Prepare for math tests in your state with these 3rd Grade to 8th Grade practice assessments for Common Core and state equivalents.

Get your 6 multiple choice practice tests with detailed answers to support test prep, created by US math teachers for US math teachers!