math

Probability A Intersection B Formula with Examples

The probability a intersection b formula is P(A ∩ B) = P(A) × P(B A), which becomes P(A)P(B) only when the events are independent. This article gives five worked examples.

Formula

math

Expected Value Formula with Worked Examples

The expected value formula is E(X) = ∑ x · P(x), each outcome multiplied by its probability and added. This article gives five worked examples.

Formula

math

Empirical Probability Formula with Examples

The empirical probability formula is P(E) = (number of times E occurred)/(total trials). This article gives five worked examples and the theoretical contrast.

Formula

math

Conditional Probability Formula with Examples

The conditional probability formula is P(B A) = (P(A ∩ B))/(P(A)), the probability of B once A is known. This article gives five worked examples.

Formula

math

Coin Toss Probability Formula with Examples

The coin toss probability formula gives any specific sequence of n fair tosses a probability of (1/2)ⁿ. This article gives five worked examples.

Formula

math

Linear Interpolation Formula with Worked Examples

The linear interpolation formula is y = y₁ + ((x-x₁)(y₂-y₁))/(x₂-x₁), estimating a value between two known points. This article gives five worked examples.

Formula

math

Prime Factorization Formula with Worked Examples

The prime factorization formula writes any integer above 1 as n = p₁ a₁ × p₂ a₂ × …, a product of prime powers. This article gives five worked examples.

Formula

math

Least Common Multiple Formula with Examples

The least common multiple formula is LCM(a,b) = (a × b)/(HCF(a,b)). This article gives the prime factorisation method, five worked examples, and the common errors.

Formula

math

Half Life Formula with Worked Examples

The half life formula is N = N₀ (1/2) t/t 1/2, halving the quantity once per half-life. This article gives five worked examples.

Formula

math

Inverse Variation Formula - Definition and Examples

The inverse variation formula is y = k/x, equivalently xy = k, so one quantity falls as the other rises. This article gives five worked examples.

Formula

math

Dividing Fractions Formula with Worked Examples

The dividing fractions formula is a/b ÷ c/d = a/b × d/c, multiplying by the reciprocal of the second fraction. This article gives five worked examples.

Formula

math

Amplitude Formula for Sine and Cosine Waves

The amplitude formula is A for y = Asin(Bx+C)+D, or equivalently (max-min)/2. This article gives five worked examples.

Formula

math

De Moivre Formula with Worked Examples

The de moivre formula states that (cosθ + isinθ)ⁿ = cos nθ + isin nθ. This article gives five worked examples including nth roots.

Formula

math

Direction of a Vector Formula with Examples

The direction of a vector formula is θ = (y/x), adjusted for the quadrant the vector lies in. This article gives five worked examples.

Formula

math

Resultant Vector Formula with Worked Examples

The resultant vector formula gives the magnitude of two combined vectors as R = √(A²+B²+2ABcosθ). This article gives five worked examples and the angle trap.

Formula

math

Maths Formula for Class 6 with Examples

Every maths formula for class 6 gathered in one place, covering perimeter, area, volume, averages, ratio and integers, with worked examples and the common errors.

Formula

math

Maths Formula for Class 8 with Examples

Every maths formula for class 8 gathered in one place, covering algebraic identities, exponent rules, mensuration and commercial arithmetic, with worked examples.

Formula

math

Maths Formula for Class 11 with Examples

Every maths formula for class 11 gathered in one place, covering sequences, trigonometry, the binomial theorem, permutations, complex numbers and conics.

Formula

math

Maths Formula for Class 12 with Examples

Every maths formula for class 12 gathered in one place, covering derivatives, integrals, vectors, three dimensional geometry and probability, with worked examples.

Formula

math

Difference of Squares Formula a2 - b2 with Examples

The difference of squares formula factors a² - b² into (a+b)(a-b). This article gives the proof, five worked examples, and why the sum of squares behaves differently.

Formula

math

Cubic Equation Formula (Cardano) with Examples

The cubic equation formula solves t³+pt+q=0 as a sum of two cube roots, after the quadratic term is removed. This article gives five worked examples.

Formula

math

Consecutive Integers Formula n, n+1, n+2 Examples

The consecutive integers formula represents them as n, n+1, n+2 and so on. This article gives the even and odd versions, five worked examples, and the sum shortcut.

Formula

math

Commutative Property Formula with Examples

The commutative property formula states a+b = b+a for addition and a × b = b × a for multiplication. This article gives five worked examples and the exceptions.

Formula

math

Clock Angle Formula with Worked Examples

The clock angle formula gives the angle between the hands as 30H - 5.5M degrees. This article gives five worked examples and the moving-hour-hand trap.

Formula

math

Square Footage Formula with Worked Examples

The square footage formula multiplies length by width with both measured in feet. This article gives five worked examples, irregular shapes, and the unit traps.

Formula

math

Slant Height Formula for Cones and Pyramids

The slant height formula for a cone is l = √(r² + h²), and for a square pyramid l = √(h² + (a/2)²). This article gives five worked examples.

Formula

math

Section Formula Class 10 with Worked Examples

The section formula class 10 gives the point dividing a segment in ratio m:n as ((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n)). This article gives five worked examples.

Formula

math

Perimeter of a Kite Formula 2(a+b) with Examples

The perimeter of a kite formula is P = 2(a+b), where a and b are the two distinct side lengths. This article gives five worked examples and the diagonal trap.

Formula

math

Height of a Parallelogram Formula - Steps and Examples

The height of a parallelogram formula divides the area by the base, h = A/b. This article gives five worked examples and why the slanted side is not the height.

Formula

math

Herons Formula for Triangle Area with Examples

Herons formula gives a triangle's area from its three sides as √(s(s-a)(s-b)(s-c)), where s is the semi-perimeter. This article gives five worked examples.

Formula

math

Diagonals Formula n(n-3)/2 with Worked Examples

The diagonals formula counts the diagonals of an n-sided polygon as (n(n-3))/2. This article gives the derivation, five worked examples, and the halving error.

Formula

math

Centroid of a Trapezoid Formula - Steps and Examples

The centroid of a trapezoid formula places the centroid at (h(2a+b))/(3(a+b)) above the base of length b. This article gives five worked examples.

Formula

math

Selling Price Formula - Definition, Steps, Examples

The selling price formula adds profit to the cost price, SP = CP + Profit, or applies a discount to the marked price. This article gives five worked examples.

Formula

math

Unit Rate Formula - Definition, Steps, Examples

The unit rate formula divides the first quantity by the second so the second becomes 1. This article gives five worked examples and the inversion error to avoid.

Formula

math

Relative Error Formula - Definition, Steps, Examples

The relative error formula divides the absolute error by the true value, ( m - t)/( t). This article gives five worked examples and the percent error link.

Formula

math

Percent Decrease Formula - Definition, Steps, Examples

The percent decrease formula divides the fall by the original value and multiplies by 100. This article gives five worked examples and why a rise and a fall never cancel.

Formula

math

Percent Difference Formula - Definition, Steps, Examples

The percent difference formula divides the absolute gap between two values by their mean, then multiplies by 100. This article gives five worked examples and the key distinctions.

Formula

math

Percentage Increase Formula - Definition, Steps, Examples

The percentage increase formula divides the rise by the original value and multiplies by 100. This article gives five worked examples and the base error that distorts answers.

Formula

math

Discount Formula - Definition, Steps, Examples

The discount formula is marked price minus selling price, and the discount percentage divides that by the marked price. This article gives five worked examples and the successive-discount trap.

Formula

math

Weighted Mean Formula - Definition, Steps, Examples

The weighted mean formula divides the total of weight times value by the total of the weights, x w = (∑ wᵢ xᵢ)/(∑ wᵢ). This article gives five worked examples.

Formula

math

Sum of Squares Formula - Definition, Proof, Examples

The sum of squares formula gives 1 squared through n squared as n(n+1)(2n+1)/6, with a proof sketch, five worked examples and the statistical meaning.

Formula

math

Sample Variance Formula - Definition, Steps, Examples

The sample variance formula divides the sum of squared deviations from the mean by n-1. This article covers the variable key, six worked examples, and why the denominator is not n.

Formula

math

Sample Standard Deviation Formula - Steps and Examples

The sample standard deviation formula takes the square root of the summed squared deviations divided by n-1. This article gives the variable key, five worked examples, and the common errors.

Formula

math

Relative Frequency Formula - Definition, Steps, Examples

The relative frequency formula divides a class frequency by the total number of observations, RF = f/n. This article gives five worked examples and the probability link.

Formula

math

Outlier Formula - IQR Fences, Z-Scores, Examples

The outlier formula flags any value below Q₁ - 1.5 × IQR or above Q₃ + 1.5 × IQR. This article covers both rules, five examples, and their limits.

Formula

math

Quartile Formula - Q1, Q2, Q3 with Examples

The quartile formula locates Q₁ at the 0.25(N+1)th ordered value and Q₃ at the 0.75(N+1)th. This article gives five worked examples and the convention warning.

Formula

math

Mean Deviation Formula - Definition, Steps, Examples

The mean deviation formula averages the absolute distances of values from the mean, dividing by n. This article gives the variable key, five worked examples, and the confusions to avoid.

Formula

math

Interquartile Range Formula (Q3 minus Q1) Examples

The interquartile range formula subtracts the first quartile from the third, IQR = Q₃ - Q₁. This article gives the quartile method, five worked examples, and the common errors.

Formula

math

Geometric Mean Formula with Worked Examples

The geometric mean formula multiplies n values and takes the nth root, GM = √[n]x₁ x₂ … xₙ. This article gives five worked examples and when to prefer it.

Formula

math

Coefficient of Variation Formula - Definition and Examples

The coefficient of variation formula divides the standard deviation by the mean, CV = s/(x). This article gives five worked examples and when the measure breaks down.

Formula

math

Kilogram to Newton Formula - Weight from Mass

The kilogram to newton formula multiplies a mass in kilograms by the acceleration of gravity, W = mg. This article gives five worked examples.

Formula

math

Yards to Meters Formula - Conversion, Steps, Examples

The yards to meters formula multiplies the yard value by 0.9144. This article gives the exact factor, a conversion table, six worked examples, and the approximation that costs accuracy.

Formula

math

mph to ms Formula : Convert Miles Per Hour to Metres Per Second

The mph to ms formula multiplies miles per hour by 0.44704. This article gives the derivation, a conversion table, six worked examples, and the compound-unit mistakes to avoid.

Formula

math

Quarts to Liters Formula (qt to L) with Examples

The quarts to liters formula multiplies US liquid quarts by 0.946352946. This article covers the Imperial and dry quart factors, a conversion table, and six worked examples.

Formula

math

Miles to Meters Formula - Conversion, Steps, Examples

The miles to meters formula multiplies the mile value by 1609.344. This article gives the exact factor, a conversion table, six worked examples, and the nautical mile mistake.

Formula

math

Liters to Gallons Formula (L to gal) with Examples

The liters to gallons formula divides litres by 3.785411784 for US gallons. This article covers the Imperial factor, a conversion table, six worked examples, and the gallon mix-up.

Formula

math

Grams to Kilograms Formula - Conversion, Steps, Examples

The grams to kilograms formula divides the gram value by 1000. This article gives the formula, a conversion table, six worked examples, and the decimal-shift mistakes to avoid.

Formula

math

Fahrenheit to Celsius Formula - Conversion, Steps, Examples

The fahrenheit to celsius formula subtracts 32, then multiplies by 5/9. This article gives the exact factors, a conversion table, six worked examples, and the mistakes that flip the answer.

Formula

math

Convert Millimeter to Inches Formula - Steps, Table, Examples

The convert millimeter to inches formula divides the millimetre value by 25.4. This article gives the exact factor, a conversion table, six worked examples, and the two mistakes that invert the answer.

Formula

math

Math Formulas: Complete List by Topic, With Examples

A math formula is a rule written in symbols that connects quantities, so you can calculate an unknown. This page lists 1,400+ math formulas by topic, each with its meaning and a worked example.

Formula