Basic Math Formulas

Mathematics is often called the “universal language.” Whether you are a student preparing for an exam, a professional managing a budget, or a homeowner measuring a room for new flooring, math is an unavoidable part of life. While modern technology gives us calculators at our fingertips, understanding the basic math formulas behind the calculations is essential for logical thinking and problem-solving.

Table of Contents

In this comprehensive guide, we have compiled the most important formulas across arithmetic, algebra, geometry, and finance to help you master the basics.

1. The Foundation: Arithmetic and Order of Operations

Before diving into complex shapes or equations, you must master the order of operations. Without this “rulebook,” two people could solve the same problem and get different answers.

The BODMAS/PEMDAS Rule

To solve any multi-step equation, follow this hierarchy:

B/P: Brackets / Parentheses
O/E: Orders (Powers/Roots) / Exponents
D/M: Division and Multiplication (left to right)
A/S: Addition and Subtraction (left to right)

Key Arithmetic Formulas:

Average (Mean): $\frac{\text{Sum of all values}}{\text{Number of values}}$
Percentage: $\left( \frac{\text{Value}}{\text{Total Value}} \right) \times 100$

2. Geometry: Measuring Space and Shapes

Geometry is one of the most practical branches of mathematics. It deals with the properties of space and the shapes that occupy it. We divide these into 2D (Area and Perimeter) and 3D (Volume and Surface Area).

2D Shapes (Flat Surfaces)

Shape	Perimeter Formula	Area Formula
Square	$4s$ (where $s$ is side)	$s^2$
Rectangle	$2(l + w)$	$l \times w$
Triangle	$a + b + c$	$\frac{1}{2} \times \text{base} \times \text{height}$
Circle	$2\pi r$ (Circumference)	$\pi r^2$

3D Shapes (Solid Objects)

Volume of a Cube: $s^3$
Volume of a Rectangular Prism: $l \times w \times h$
Volume of a Sphere: $\frac{4}{3}\pi r^3$
Volume of a Cylinder: $\pi r^2 h$

3. Algebra: Solving for the Unknown

Algebra allows us to take real-world problems and turn them into equations where we solve for a variable, usually represented as $x$ .

Important Algebraic Identities

These formulas are shortcuts for expanding or simplifying equations:

Square of a Sum: $(a + b)^2 = a^2 + 2ab + b^2$
Square of a Difference: $(a - b)^2 = a^2 - 2ab + b^2$
Difference of Squares: $a^2 - b^2 = (a - b)(a + b)$

The Quadratic Formula

When you have a quadratic equation in the form $ax^2 + bx + c = 0$ , you can find the value of $x$ using:

x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

4. Trigonometry: The Math of Triangles

Trigonometry is vital for architecture, engineering, and physics. It focuses on the relationship between the angles and sides of triangles, specifically right-angled triangles.

The Pythagorean Theorem

In any right-angled triangle, the square of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides:

a^2 + b^2 = c^2

SOH-CAH-TOA

To find missing angles or sides, we use these ratios:

Sine (Sin): $\frac{\text{Opposite}}{\text{Hypotenuse}}$
Cosine (Cos): $\frac{\text{Adjacent}}{\text{Hypotenuse}}$
Tangent (Tan): $\frac{\text{Opposite}}{\text{Adjacent}}$

5. Financial Math: Managing Your Money

Understanding math formulas can literally save you money. Whether you are calculating the interest on a bank loan or a discount at a store, these formulas are key.

Simple Interest

This is the interest calculated only on the initial amount of money (the principal) you invest or borrow.

I = P \times R \times T

(Where $P$ = Principal, $R$ = Rate of interest, $T$ = Time)

Compound Interest

Most modern banks use compound interest, where you earn interest on your interest.

A = P \left(1 + \frac{r}{n}\right)^{nt}

(Where $A$ = Total amount, $n$ = number of times interest is compounded per year)

Why Memorizing Formulas Still Matters in 2026

Even with AI and advanced computers, knowing these formulas provides “mental shortcuts.” It allows you to estimate costs, understand architectural designs, and analyze data without needing a screen. For students in Bangladesh and around the world, mastering these basics is the first step toward high-paying careers in Engineering, Data Science, and Finance.