Formula Library

53 formulas with definitions, variables, examples, and linked calculators.

Complete Formula Reference

This library contains 49 essential formulas from mathematics, physics, chemistry, statistics, finance, geometry, and unit conversion. Each entry includes the equation, variable definitions, a worked example, tips, and a linked calculator.

How to Use This Library

Find your formula by category below or in the card grid
Read the definition and variable meanings on the formula page
Study the worked example to understand the calculation
Click the linked calculator to solve with your own values

All Formulas by Category

Algebra

Formula	Equation	Example
Quadratic Formula	`x = (-b +/- sqrt(b^2 - 4ac)) / 2a`	For x^2-5x+6=0: x=2 or x=3
Linear Equation	`ax + b = 0, x = -b/a`	2x+6=0 gives x=-3

Geometry

Formula	Equation	Example
Pythagorean Theorem	`a^2 + b^2 = c^2`	a=3, b=4, c=5
Slope Formula	`m = (y2 - y1) / (x2 - x1)`	Points (1,2) and (3,6) give m=2
Distance Formula	`d = sqrt((x2-x1)^2 + (y2-y1)^2)`	(0,0) to (3,4) gives d=5
Circle Area	`A = pi * r^2`	Radius 5 gives A about 78.54
Circumference	`C = 2 * pi * r`	Radius 5 gives C about 31.42
Triangle Area	`A = 0.5 * base * height`	Base 10, height 6 gives A=30
Sphere Volume	`V = (4/3) * pi * r^3`	Radius 3 gives V about 113.1
Cylinder Volume	`V = pi * r^2 * h`	r=2, h=5 gives V about 62.83
Sphere Surface Area	`SA = 4 * pi * r^2`	r=3 gives SA about 113.1
Rectangle Area	`A = length * width`	5 by 8 = 40 square units
Arc Length	`s = r * theta (radians)`	r=5, theta=pi/2

Statistics

Formula	Equation	Example
Standard Deviation	`s = sqrt(Sum(x - mean)^2 / (n-1))`	Sample std dev of 2,4,4,5,7,9 is about 2.14
Z-Score	`z = (x - mean) / std_dev`	x=85, mean=75, sd=10 gives z=1
Variance	`variance = sum((x-mean)^2) / (n-1)`	Square of standard deviation
Permutation	`nPr = n! / (n-r)!`	10P3 = 720
Combination	`nCr = n! / (r!(n-r)!)`	10C2 = 45
Confidence Interval	`CI = mean +/- z * (s/sqrt(n))`	95% confidence uses z about 1.96
Pearson Correlation	`r = cov(x,y) / (sx * sy)`	r ranges from -1 to +1
Linear Regression	`y = m*x + b`	Use regression calculator
Basic Probability	`P = favorable / total outcomes`	Rolling a 6: P=1/6

Finance

Formula	Equation	Example
Compound Interest	`A = P(1 + r/n)^(nt)`	$1000 at 5% for 10 years
EMI Formula	`EMI = Pr(1+r)^n / ((1+r)^n - 1)`	Use EMI calculator for loan examples
Simple Interest	`I = P * r * t`	$1000 at 5% for 2 years = $100
Profit Margin	`Margin = (Revenue-Cost)/Revenue * 100%`	Use profit margin calculator
Discount Formula	`Sale = Price * (1 - discount/100)`	20% off $50 = $40

Physics

Formula	Equation	Example
Ohm's Law	`V = I * R`	12V, 4 ohms gives 3A
Kinetic Energy	`KE = 0.5 * m * v^2`	2kg at 3m/s gives KE=9J
Potential Energy	`PE = m * g * h`	1kg at 10m gives PE about 98.1J
Force Formula	`F = m * a`	10kg times 2m/s^2 equals 20N
Velocity Formula	`v = d / t`	100m in 10s gives 10m/s
Density Formula	`density = mass / volume`	500g in 250cm^3 gives 2g/cm^3
Electrical Power	`P = V * I`	Also P = I^2 * R
Work Formula	`W = F * d`	10N over 5m = 50J
Momentum	`p = m * v`	2kg at 3m/s = 6 kg m/s

Math

Formula	Equation	Example
Percentage Formula	`X% of Y = (X/100) * Y`	20% of 150 = 30
Exponent Rules	`a^m * a^n = a^(m+n)`	2^3 times 2^2 equals 2^5 = 32
Logarithm Rules	`log(xy) = log(x) + log(y)`	log(10)+log(2)=log(20)
GCF Euclidean Algorithm	`GCD via repeated remainder division`	GCF(48,18)=6
LCM Formula	`LCM(a,b) = \|a*b\| / GCF(a,b)`	LCM(4,6)=12
Percent Error	`% error = \|expected-actual\|/\|expected\|*100`	Use percent error calculator
Significant Figures	`Count meaningful digits by standard rules`	0.00450 has 3 sig figs

Chemistry

Formula	Equation	Example
pH Formula	`pH = -log10[H+]`	10^-7 M gives pH=7
Dilution Formula	`C1V1 = C2V2`	Use dilution calculator for lab prep
Molarity	`M = moles / volume(L)`	0.5 mol in 2L gives 0.25M

Converters

Formula	Equation	Example
Celsius to Fahrenheit	`F = (C * 9/5) + 32`	100C = 212F
Meters to Feet	`feet = meters * 3.28084`	1 meter about 3.28 feet
Kilograms to Pounds	`lb = kg * 2.20462`	70kg about 154.32 lb