20 Important Math Formulas Students Should Know

Virginia
June 21, 2022

As any student knows, tough math problems are difficult enough without needing to remember the right formula. So, it’s important to have all the right tools in their back pocket!

Remembering the step-by-step methodology required to solve complex math problems is demanding enough for students. The last thing they need is to try and recall a tricky formula on top of that!

Whether your child needs to brush up to tackle their homework or needs to remember the essentials for a big test or quiz, these formulas are sure to come in handy.

Important Math Formulas

First, a chart of the different important formulas to make things easier! If you want more details for each one, continue reading below.

Formula Name	Formula	Application
Area of Rectangle	Area = length × width	Used to find the area of a rectangle.
Perimeter of Rectangle	Perimeter = 2(l + b)	Used to find the total outer length of a rectangle.
Area of Square	Area = a²	Used to find the area of a square.
Perimeter of Square	Perimeter = 4 × a	Used to find the total perimeter of a square.
Area of Circle	Area = π × r²	Used to calculate the area of a circular shape.
Circumference of Circle	Circumference = 2π × r	Used to determine the boundary length of a circle.
Average	Average = (Sum of values) / (Number of values)	Determines the average of a data set.
Quadratic Formula	x = −b ± √(b²-4ac) / 2a	Solves quadratic equations in algebra.
Probability	Probability = (Favorable outcomes) / (Total outcomes)	Calculates the likelihood of an event occurring.
Distance Formula	d = √((x₁ – x₂)² + (y₁ – y₂)²)	Finds the distance between two points in a plane.
Slope Formula	Slope = (y₂ – y₁) / (x₂ – x₁)	Finds the slope of a line connecting two points.
Slope Intercept Formula	y = mx + b	Finds the slope-intercept form of a line.
Area of Triangle	Area = ½ × base × height	Calculates the area of a triangle.
Sine (SOH)	sin(θ) = opposite / hypotenuse	Finds unknown angles in a right triangle.
Cosine (CAH)	cos(θ) = adjacent / hypotenuse	Finds unknown angles in a right triangle.
Tangent (TOA)	tan(θ) = opposite / adjacent	Finds unknown angles in a right triangle.
Pythagorean Theorem	a² + b² = c²	Finds the length of a hypotenuse in a right triangle.
Standard Form of a Complex Number	z = a + bi	Represents a complex number.
Modulus of a Complex Number	\|z\| = √(a² + b²)	Finds the modulus (magnitude) of a complex number.
Conjugate of a Complex Number	z̄ = a - bi	Finds the conjugate of a complex number.

Elementary & Middle School

1. Area of Rectangle: area = length x width

Kids will need to know this one in pre-algebra and later math classes.

2. Perimeter of a rectangle: 2(l + b)

This will calculate the total of the outer lines of a rectangle.

3. Area of a square: a²

Square the length of both sides to find the area of a square.

4. Perimeter of a square: 4 x a

Multiply the length of the side of the square by 4 to find the perimeter.

5. Area of a circle: π x r²

Use this to find the total area of a circle.

6. Circumference of a circle: 2π x r

This formula calculates the length of the outside of a circle.

7. Find the Average: Sum of total numbers divided by the number of values.

Useful in statistics and many more math word problems.

Useful High School and SAT® Math Formulas

These high school math formulas will come in handy in geometry, algebra, calculus and more. Plus, when SAT® season arrives, they will help teens succeed on the challenging math section.

(Looking for more SAT® math help? Check out 11 SAT® Apps for Daily Practice and How to Study for a Math Test.)

8. The Quadratic Formula: x = −b ± √b²-4ac/2a

Students will need this to solve quadratic equations in algebra II and beyond. As an added pneumonic bonus, it’s easier to remember this one to the tune of “Pop Goes the Weasel”.

9. Probability: Number of favorable outcomes divided by the total number of favorable outcomes.

To determine the probability of an event, this equation will determine the odds of something happening.

10. Distance formula: d=√(x₁ – x₂)² + (y₁ – y₂)²

This equation will calculate the distance between two points, which will be necessary in geometry and algebra.

11. Slope Formula: Slope = y₂ – y₁ / x₂ – x₁

Use this to find the angle that joins two points on a graph.

12. Slope Intercept Formula: y=mx+b

In algebra, this will find the slope intercept of a straight line.

13. Area of Triangle: Area = (1/2) (base) (height)

Use this in geometry to find the total area of a triangle.

14. Sine (SOH): Sine = opposite / hypotenuse

This equation calculates the unknown angles of a triangle.

15. Cosine (CAH): Cosine = adjacent / hypotenuse

Use this equation to find the unknown angles of a triangle.

16. Tangent (TOA): Tangent = opposite / adjacent

This equation also can be used to calculate the unknown angles of a triangle.

17. The Pythagorean Theorem: a²+b²=c²

This is used to find the length of a hypotenuse in a right triangle. In any right triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the legs of the right triangle.

Complex Number Formulas

These complex number formulas are essential for mastering advanced algebra, trigonometry, and geometry. Whether tackling high school math, preparing for the SAT®, or exploring higher-level math concepts, these tools will simplify challenging problems and build a strong foundation.

18. Standard Form of a Complex Number: z = a +bi

Where a is the real part, and b is the imaginary part.

19. Modulus of a Complex Number: |z| = √a²+b²

This equation calculates the distance of the complex number from the origin in the complex plane.

20. Conjugate of a Complex Number: z̄ = a - bi

This formula is useful in rationalizing denominators or simplifying expressions.

Got math problems? We’ve got math solutions!

In addition to unparalleled math tutoring, iD Tech offers a wealth of math resources. Here’s a sneak peek:

With these helpful tips and tricks in hand, you’re ready to support your student with math homework, tests, quizzes, and the SAT®!

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Virginia

Virginia started with iD Tech at the University of Denver in 2015 and has loved every minute since then! A former teacher by trade, she has a master's in education and loves working to embolden the next generation through STEM. Outside the office, you can usually find her reading a good book, struggling on a yoga mat, or exploring the Rocky Mountains.

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20 Important Math Formulas Students Should Know

Important Math Formulas

Elementary & Middle School

1. Area of Rectangle: area = length x width

2. Perimeter of a rectangle: 2(l + b)

3. Area of a square: a²

4. Perimeter of a square: 4 x a

5. Area of a circle: π x r²

6. Circumference of a circle: 2π x r

7. Find the Average: Sum of total numbers divided by the number of values.

Useful High School and SAT® Math Formulas

8. The Quadratic Formula: x = −b ± √b²-4ac/2a

9. Probability: Number of favorable outcomes divided by the total number of favorable outcomes.

10. Distance formula: d=√(x₁ – x₂)² + (y₁ – y₂)²

11. Slope Formula: Slope = y₂ – y₁ / x₂ – x₁

12. Slope Intercept Formula: y=mx+b

13. Area of Triangle: Area = (1/2) (base) (height)

14. Sine (SOH): Sine = opposite / hypotenuse

15. Cosine (CAH): Cosine = adjacent / hypotenuse

16. Tangent (TOA): Tangent = opposite / adjacent

17. The Pythagorean Theorem: a²+b²=c²

Complex Number Formulas

18. Standard Form of a Complex Number: z = a +bi

19. Modulus of a Complex Number: |z| = √a²+b²

20. Conjugate of a Complex Number: z̄ = a - bi

Got math problems? We’ve got math solutions!

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