Math Formula

Interest Formula – Simple & Compound Interest Explained

This article derives and applies both the simple and compound interest formula, walking through every variable, showing worked examples, and explaining when each formula applies in real financial contexts. You will leave able to calculate interest on savings, loans, and investments — and to spot which formula a problem is actually asking for.

Circle Area Formulas – Class 10 Complete Guide

This reference guide collects every circle area formula you need for Class 10 — full circle, semicircle, sector, ring, and segment — with derivations, variable keys, and fully worked examples for each. You will have a single reliable source to consult before any exam that tests circular mensuration.

Correlation Coefficient Formula & Calculation

This article explains the correlation coefficient formula — Pearson's r — from its definition through the step-by-step calculation, with a worked numerical example and guidance on interpreting the result. You will understand what r measures, how to compute it by hand, and how to avoid the most common misreading of correlation as causation.

Time Formula – Speed, Distance & Time Explained

This article explains the time formula — Time = Distance ÷ Speed — alongside its speed and distance variants, with a worked-example bank covering unit conversions, average speed, and multi-stage journey problems. You will leave confident applying all three forms of the speed-distance-time relationship in any exam or real-life scenario.

Profit Formula – How to Calculate Profit Easily

This article explains the profit formula — Profit = Selling Price − Cost Price — alongside gross profit, net profit, and profit percentage, with clear worked examples for each variation. You will learn how to calculate profit easily for both straightforward transactions and multi-cost business scenarios.

Perimeter of a Circle Formula – Circumference Guide

The perimeter of a circle formula (circumference) explained — derivation, the role of π, variable key, worked examples, and the difference between diameter and radius forms.

Sin 2x Formula – Derivation, Values & Examples

This article derives the sin 2x formula — sin 2x = 2 sin x cos x — from the angle addition identity, tabulates key values, and works through exam-style problems that use the double-angle identity to simplify expressions and solve equations. You will understand where the formula comes from and when to apply it.

Profit and Loss Formula – Calculation & Examples

This guide covers the profit and loss formula in full — profit, loss, profit percentage, loss percentage, cost price, and selling price — with step-by-step worked examples drawn from realistic retail and exam contexts. By the end you will be able to calculate any profit-and-loss problem accurately and identify which formula a question is testing.

Cube Formula – Volume, Surface Area & Diagonal

This guide covers every cube formula you need — volume, total surface area, lateral surface area, face diagonal, and space diagonal — each derived from first principles and illustrated with a worked example. After reading you will be able to solve any standard exam question on cubes without looking up a formula sheet.

Celsius to Fahrenheit Formula – Quick Conversion

Work Formula – Physics & Math Definition

Average Speed Formula: Calculation & Examples

Average speed formula is not the simple average of two speeds, except when each speed is travelled for the same time. For two equal distances at speeds $v_1$ and $v_2$, average speed is the harmonic mean: $\dfrac{2 v_1 v_2}{v_1 + v_2}$.

nCr Formula – Combinations, Proof & Examples

The nCr formula gives the number of ways to choose r items from n when order does not matter. Use it for committees, lottery tickets, card hands, lineup picks - any pick where rearranging the chosen items does not create a new pick.

Surface Area Formulas: All 3D Shapes Covered

Surface area is the total area covering the outside of a 3D shape, measured in square units. Each 3D shape has its own formula, but they all come from the same idea - unfold the shape into flat pieces, find each piece's area, and add them up.

Frequency Formula: Definition, Units, and Examples

*Frequency** is the number of complete cycles that happen in one unit of time. **The formula:** $f = \dfrac{1}{T}$, where $T$ is the time for one cycle (the period). **SI unit:** hertz (Hz). One hertz = one cycle per second.

Derivative Formula: Rules, List & Examples

The **derivative formula**, $f'(x) = \lim_{h \to 0} \dfrac{f(x+h) - f(x)}{h}$, measures a function's instantaneous rate of change at a single point, applied through standard rules — power, sum, product, quotient, and chain — together with the derivatives of trig, exponential, logarithmic, and inverse trig functions, with the chain rule and the product rule causing most student errors.

Tangent Formulas: All Tan Identities & Values

The tangent formula defines $\tan(\theta)$ as the ratio of the opposite side to the adjacent side in a right triangle, equivalently $\sin(\theta) / \cos(\theta)$ on the unit circle. Every other tangent identity — sum, double, half, reciprocal, Pythagorean — is built from that single ratio with a small amount of algebra.

Sin Cos Tan Formula: Ratios, Values & Examples

The sin cos tan formula describes three ratios of sides in a right triangle, one for each acute angle. The mnemonic SOH-CAH-TOA captures all three. Standard values at 0°, 30°, 45°, 60°, and 90° are memorised once and reused everywhere - from solving triangles to satellite navigation to music synthesis.

Average Formula: Mean Calculation & Examples

The average formula is Average = Sum of all values ÷ Number of values, which collapses a list of numbers into one representative number called the mean. Add every value, divide by how many values you added, and the result is the average.

Log Formulas: All Logarithm Rules & Examples

A logarithm answers one question: what power do I raise the base to in order to get this number? Every log formula on this page comes from rewriting that question.

Cosine Formulas: All Cos Identities & Values

Cosine formulas come from one definition ($\cos\theta = \text{adjacent}/\text{hypotenuse}$) and one parent identity ($\cos(A+B) = \cos A \cos B - \sin A \sin B$). Every other cosine formula — difference, double angle, half angle, product-to-sum, law of cosines — is one substitution away.

Binomial Expansion Formula: Theorem, Examples & Solved Problems

The binomial expansion formula gives the expanded form of (x + y)ⁿ as a sum of n + 1 terms involving binomial coefficients. The general formula is (x + y)ⁿ = Σ ⁿCₖ xⁿ⁻ᵏ yᵏ, where ⁿCₖ = n! / [k!(n − k)!]. It is used to expand any binomial raised to a positive integer, fractional, or negative power without multiplying the binomial by itself n times.

Mean, Median, Mode Formula - Differences, Use, and Examples

The mean is the average of all values (Σx / n), the median is the middle value when data is ordered, and the mode is the value that appears most often. Use the mean for symmetric data, the median for skewed data with outliers, and the mode for categorical data. For moderately skewed distributions, the three are linked by Karl Pearson's empirical relation: Mode = 3 Median − 2 Mean.

Perimeter Formulas: All Shapes with Variables and Worked Examples

The perimeter of a 2D shape is the total length of its boundary — found by adding the lengths of all its sides. Common shortcuts include P = 4a (square), P = 2(l + w) (rectangle), and C = 2πr (circle).

Triangle Formula: Area, Perimeter, and All Types Explained

The most common triangle formulas are A = ½ × base × height for area and P = a + b + c for perimeter. Other formulas - Heron's formula, the trigonometric area formula, and per-type formulas for equilateral, isosceles, and right triangles - apply depending on what information you have. The decision table further down shows which formula to use in which case.

Geometric Sequence Formulas: nth Term, Sum, and Examples

The geometric sequence formulas cover three things: the nth term aₙ = a · r^(n−1), the sum of the first n terms Sₙ = a(1 − rⁿ)/(1 − r) for r ≠ 1, and the infinite sum S∞ = a/(1 − r) when |r| < 1. The first formula finds any single term; the other two add up multiple terms.

Arithmetic Sequence Formula: nth Term, Sum & Common Difference

The arithmetic sequence formula has two parts: aₙ = a₁ + (n−1)d for the nth term and Sₙ = (n/2) × [2a₁ + (n−1)d] for the sum of n terms. Here a₁ is the first term, d is the common difference, and n is the position. Use (n−1) - not n - when counting the jumps between terms.

Double Angle Formulas: Sin, Cos, Tan Identities

The double angle formulas are sin 2θ = 2 sin θ cos θ, cos 2θ = cos²θ − sin²θ (also 1 − 2 sin²θ and 2 cos²θ − 1), and tan 2θ = 2 tan θ / (1 − tan²θ). All three are derived from the sum formulas by setting α = β = θ. The cosine has three equivalent forms because the Pythagorean identity converts between them.

Volume Formulas for All 3D Shapes

Volume measures the space a 3D shape occupies, expressed in cubic units (cm³, m³, in³). Each shape has its own formula - cube uses V = a³, cuboid uses l × b × h, cylinder uses πr²h, sphere uses ⁴⁄₃ πr³, and cones and pyramids hold exactly one-third of their corresponding cylinder or prism.

Slope Formula: How to Find the Slope of a Line

The slope formula is m = (y₂ − y₁) / (x₂ − x₁) - it calculates the steepness and direction of a line from any two points on it. Slope can be positive (line rises), negative (line falls), zero (horizontal), or undefined (vertical). The formula is also written as rise over run, where rise = Δy and run = Δx.

Distance Formula in Maths: Definition, Derivation, and Examples

The distance formula, d = √[(x₂ − x₁)² + (y₂ − y₁)²], gives the straight-line distance between two points on a coordinate plane. It is derived from the Pythagorean theorem and extends to 3D by adding a z-coordinate term.

Geometry Formulas: Area, Perimeter & Volume for 2D and 3D Shapes

Geometry formulas calculate the perimeter and area of 2D shapes (square, rectangle, triangle, circle) and the surface area and volume of 3D shapes (cube, cuboid, cylinder, cone, sphere). Perimeter uses linear units (cm), area and surface area use square units (cm²), and volume uses cubic units (cm³).

Integration Formulas: Complete List with Examples

Integration formulas are the standard antiderivative results used to solve integrals across Class 11, 12, and JEE - covering basic, trigonometric, inverse trigonometric, exponential, logarithmic, hyperbolic, and special integrals. The general form is ∫f'(x) dx = f(x) + C.