Reference Sheet

Formula Reference Sheet

A student-friendly quick reference for common formulas used in math, science, finance, measurement, and classroom problem solving.

Open Scientific Calculator Open Unit Converter Geometry Reference
Use Ctrl+F or the search box to find a formula quickly.

Number Sense & Percent

Percent of a number
part = percent × wholeChange percent to a decimal first. Example: 20% = 0.20.
Percent
percent = part ÷ wholeConvert the decimal answer to a percent.
Percent change
(new − old) ÷ oldPositive means increase; negative means decrease.
Average / Mean
mean = sum of values ÷ number of valuesAdd all values, then divide by how many values there are.
Unit rate
unit rate = amount ÷ unitsExample: miles per hour, dollars per item, words per minute.

Algebra & Graphing

Slope
m = (y₂ − y₁) ÷ (x₂ − x₁)Rise over run between two points.
Slope-intercept form
y = mx + bm is slope; b is the y-intercept.
Distance on coordinate plane
d = √((x₂ − x₁)² + (y₂ − y₁)²)Finds distance between two points.
Midpoint
((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2)The point halfway between two points.
Quadratic formula
x = (-b ± √(b² − 4ac)) ÷ 2aUsed for ax² + bx + c = 0.

Common Measurement

Rectangle area
A = l × wLength times width.
Triangle area
A = ½bhb is base; h is height.
Circle circumference
C = 2πrDistance around a circle.
Circle area
A = πr²r is radius.
Rectangular prism volume
V = l × w × hLength times width times height.

Science Formulas

Speed
speed = distance ÷ timeCommon units: mph, m/s, km/h.
Distance
distance = speed × timeUseful for motion problems.
Density
density = mass ÷ volumeCommon units: g/mL or g/cm³.
Force
F = m × aForce equals mass times acceleration.
Work
W = F × dWork equals force times distance.

Money & Practical Math

Simple interest
I = P × r × tP is principal, r is rate as decimal, t is time.
Total with simple interest
A = P + IAmount equals principal plus interest.
Discount price
sale price = original − discountFind the discount amount first.
Sales tax
total = price + taxTax = price × tax rate.
Tip
tip = bill × tip rateExample: 18% = 0.18.

Probability & Statistics

Probability
P(event) = favorable outcomes ÷ total outcomesAnswer can be fraction, decimal, or percent.
Range
range = highest − lowestShows spread of a data set.
Median
middle valuePut values in order first.
Mode
most frequent valueA set can have no mode or more than one mode.
Formulas are helpful, but students still need to choose the correct formula, identify the values, use consistent units, and check whether the answer makes sense.