Math formulas are the essential building blocks you need to...
Algebra 1293 views·Updated Aug 4, 2026·4 pagesUnderstanding Math Functions
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1
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Essential Math Formulas
Ever wonder how to find the distance between two points or figure out a parabola's vertex? These formulas are your toolkit for solving coordinate geometry and algebra problems.
The distance formula helps you find how far apart two points are: √. When you need the point exactly between two locations, use the midpoint formula: .
For lines, the slope formula (rise/run) is /. You can write equations using point-slope form or the simpler slope-intercept form . When dealing with parabolas, the quadratic formula /2a solves for the x-intercepts of y=ax²+bx+c.
Pro Tip: To find where a parabola reaches its highest or lowest point (the vertex), use x=-b/2a, then plug that x-value into the original equation to find y.
2
of 4
Area and Perimeter Formulas
Need to calculate how much fencing for a yard or paint for a wall? These formulas will help you find the space inside (area) and distance around (perimeter) different shapes.
For squares and rectangles, area is straightforward: square area is s² (side squared), while rectangle area is l×w (length times width). Triangle area is ½(b×h) – half the base times the height. For circles, area equals πr² (pi times radius squared).
When calculating perimeters, square perimeter equals 4s (four sides), rectangle perimeter is 2l+2w (twice length plus twice width), and triangle perimeter is the sum of all three sides. The distance around a circle, called circumference, equals 2πr.
Remember: For irregular shapes like trapezoids , break them down into simpler shapes you already know how to calculate!
3
of 4
Volume and Surface Area
When you jump into 3D shapes, you'll need formulas to find how much space is inside (volume) and how much material covers the outside (surface area).
A sphere's volume is πr³, while a cone's volume is πr²h. For containers like cylinders, volume equals πr²h, and a rectangular prism's volume is simply l×w×h (length × width × height).
Surface area calculations help you determine how much wrapping paper you'd need for a box or paint for a tank. A sphere's surface area is 4πr², a cylinder's surface area is 2πrh+2πr² (curved side plus two circular ends), and a rectangular prism's surface area is 2(wl+hl+hw).
Visualization Tip: Think of volume as how many cubes fit inside a shape, while surface area is like unfolding the shape and measuring its "skin."
4
of 4
Logarithmic and Exponential Formulas
Logarithms and exponentials might seem tricky at first, but they're super useful for problems involving growth, decay, and solving certain equations.
The log product rule (logₐ(P·Q) = logₐP + logₐQ) lets you split a logarithm of multiplied numbers. When dividing inside a logarithm, use the log quotient rule: logₐ(P/Q) = logₐP - logₐQ. For exponents inside logarithms, the log power rule states logₐ = q·logₐP.
With exponentials, remember that multiplying the same base with different exponents means you add the exponents: a^m·a^n = a^. When dividing exponentials with the same base, subtract the exponents: a^m/a^n = a^.
Real-World Connection: These formulas are crucial for understanding compound interest, population growth, and radioactive decay. For example, the amount in a bank account with compound interest can be calculated using P^(nt).
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Algebra 1293 views·Updated Aug 4, 2026·4 pagesUnderstanding Math Functions
Math formulas are the essential building blocks you need to solve problems across different areas of mathematics. This guide provides key formulas for geometry, algebra, and more that will help you solve problems quickly and accurately.
1
of 4
Sign up to see the content. It's free!
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- Improve your grades
- Join milions of students
Essential Math Formulas
Ever wonder how to find the distance between two points or figure out a parabola's vertex? These formulas are your toolkit for solving coordinate geometry and algebra problems.
The distance formula helps you find how far apart two points are: √. When you need the point exactly between two locations, use the midpoint formula: .
For lines, the slope formula (rise/run) is /. You can write equations using point-slope form or the simpler slope-intercept form . When dealing with parabolas, the quadratic formula /2a solves for the x-intercepts of y=ax²+bx+c.
Pro Tip: To find where a parabola reaches its highest or lowest point (the vertex), use x=-b/2a, then plug that x-value into the original equation to find y.
2
of 4Sign up to see the content. It's free!
- Access to all documents
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Area and Perimeter Formulas
Need to calculate how much fencing for a yard or paint for a wall? These formulas will help you find the space inside (area) and distance around (perimeter) different shapes.
For squares and rectangles, area is straightforward: square area is s² (side squared), while rectangle area is l×w (length times width). Triangle area is ½(b×h) – half the base times the height. For circles, area equals πr² (pi times radius squared).
When calculating perimeters, square perimeter equals 4s (four sides), rectangle perimeter is 2l+2w (twice length plus twice width), and triangle perimeter is the sum of all three sides. The distance around a circle, called circumference, equals 2πr.
Remember: For irregular shapes like trapezoids , break them down into simpler shapes you already know how to calculate!
3
of 4Sign up to see the content. It's free!
- Access to all documents
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Volume and Surface Area
When you jump into 3D shapes, you'll need formulas to find how much space is inside (volume) and how much material covers the outside (surface area).
A sphere's volume is πr³, while a cone's volume is πr²h. For containers like cylinders, volume equals πr²h, and a rectangular prism's volume is simply l×w×h (length × width × height).
Surface area calculations help you determine how much wrapping paper you'd need for a box or paint for a tank. A sphere's surface area is 4πr², a cylinder's surface area is 2πrh+2πr² (curved side plus two circular ends), and a rectangular prism's surface area is 2(wl+hl+hw).
Visualization Tip: Think of volume as how many cubes fit inside a shape, while surface area is like unfolding the shape and measuring its "skin."
4
of 4Sign up to see the content. It's free!
- Access to all documents
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Logarithmic and Exponential Formulas
Logarithms and exponentials might seem tricky at first, but they're super useful for problems involving growth, decay, and solving certain equations.
The log product rule (logₐ(P·Q) = logₐP + logₐQ) lets you split a logarithm of multiplied numbers. When dividing inside a logarithm, use the log quotient rule: logₐ(P/Q) = logₐP - logₐQ. For exponents inside logarithms, the log power rule states logₐ = q·logₐP.
With exponentials, remember that multiplying the same base with different exponents means you add the exponents: a^m·a^n = a^. When dividing exponentials with the same base, subtract the exponents: a^m/a^n = a^.
Real-World Connection: These formulas are crucial for understanding compound interest, population growth, and radioactive decay. For example, the amount in a bank account with compound interest can be calculated using P^(nt).
We thought you’d never ask...
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
You can download the app in the Google Play Store and in the Apple App Store.
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Students love us — and so will you.
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Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
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