Slope between two points
$$m=\frac{y_2-y_1}{x_2-x_1}$$
Measure vertical change per unit of horizontal change.
High schoolAlgebra formulas, grouped by topic.
28 algebra formulas across 11 topics, free and without an account. Algebra formulas describe structure: how a line is determined, how a quadratic factors, how exponents and logarithms undo one another, and how a sequence continues. Most of them are identities that hold for every allowed value, which is why they can be applied in either direction — expanding when you need to compute, factoring when you need roots. The conditions almost always come down to a denominator or a base that must not vanish.
Every algebra formula on one page
Each entry links to its own page, where the symbols are defined, the conditions are stated, and the formula is substituted through a worked example. Levels covered here: Middle school, High school, AP.
Lines
4 formulas in lines.
Slope-intercept form
$$y=mx+b$$
Write a nonvertical line using its slope and vertical intercept.
High schoolPoint-slope form
$$y-y_1=m(x-x_1)$$
Write a line from one point and its slope.
High schoolStandard form of a line
$$Ax+By=C$$
Represent horizontal, vertical, and slanted lines in one form.
High schoolQuadratics
4 formulas in quadratics.
Quadratic formula
$$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$
Find every real or complex root of a quadratic equation.
High school · APDiscriminant
$$\Delta=b^2-4ac$$
Predict the number and type of roots before solving a quadratic.
High schoolQuadratic vertex
$$x_v=-\frac{b}{2a},\qquad y_v=f(x_v)$$
Locate the turning point of a parabola in standard form.
High schoolCompleting the square
$$x^2+bx=\left(x+\frac b2\right)^2-\left(\frac b2\right)^2$$
Rewrite a quadratic expression as a square plus or minus a constant.
High schoolFactoring
2 formulas in factoring.
Difference of squares
$$a^2-b^2=(a-b)(a+b)$$
Factor a subtraction of two perfect squares.
High schoolSum and difference of cubes
$$a^3\pm b^3=(a\pm b)(a^2\mp ab+b^2)$$
Factor a sum or difference of perfect cubes.
High schoolExponents
3 formulas in exponents.
Product and quotient powers
$$a^m a^n=a^{m+n},\qquad \frac{a^m}{a^n}=a^{m-n}$$
Combine powers that have the same base.
High schoolPower of a power
$$(a^m)^n=a^{mn}$$
Raise an existing power by multiplying exponents.
High schoolZero and negative exponents
$$a^0=1,\qquad a^{-n}=\frac1{a^n}$$
Interpret zero and negative integer powers.
Middle school · High schoolRadicals
1 formula in radicals.
Rational exponent
$$a^{m/n}=\sqrt[n]{a^m}$$
Translate between radical notation and fractional exponents.
High schoolSequences
4 formulas in sequences.
Arithmetic sequence term
$$a_n=a_1+(n-1)d$$
Find a term in a sequence with constant difference.
High schoolArithmetic series sum
$$S_n=\frac{n}{2}(a_1+a_n)=\frac{n}{2}\left[2a_1+(n-1)d\right]$$
Add the first $n$ terms of an arithmetic sequence.
High schoolGeometric sequence term
$$a_n=a_1r^{n-1}$$
Find a term in a sequence with constant ratio.
High schoolFinite geometric series
$$S_n=a_1\frac{1-r^n}{1-r}$$
Add the first $n$ terms of a geometric sequence.
High school · APLogarithms
3 formulas in logarithms.
Logarithm definition
$$\log_b x=y\iff b^y=x$$
Translate between logarithmic and exponential statements.
High schoolLog product and quotient rules
$$\log_b(MN)=\log_bM+\log_bN,\quad\log_b\frac{M}{N}=\log_bM-\log_bN$$
Expand or combine logarithms of products and quotients.
High schoolChange of base
$$\log_b x=\frac{\ln x}{\ln b}=\frac{\log_a x}{\log_a b}$$
Evaluate a logarithm using a different available base.
High schoolGrowth
1 formula in growth.
Exponential growth and decay
$$A=A_0e^{kt}$$
Model continuous proportional growth or decay.
High school · APPolynomials
3 formulas in polynomials.
Product of two binomials
$$(a+b)(c+d)=ac+ad+bc+bd$$
Expand a product by multiplying every term in one binomial by every term in the other.
Middle school · High schoolBinomial theorem
$$(x+y)^n=\sum_{k=0}^{n}\binom nkx^{n-k}y^k$$
Expand a nonnegative integer power of a binomial.
High school · APRemainder theorem
$$\text{remainder of }f(x)\div(x-a)=f(a)$$
Find a linear-division remainder without performing long division.
High schoolVariation
2 formulas in variation.
Direct variation
$$y=kx$$
Model two quantities whose ratio stays constant.
Middle school · High schoolInverse variation
$$y=\frac{k}{x},\qquad xy=k$$
Model two quantities whose product stays constant.
High schoolSystems
1 formula in systems.
Two-variable linear system
$$\begin{aligned}a_1x+b_1y&=c_1\\a_2x+b_2y&=c_2\end{aligned}\quad x=\frac{c_1b_2-b_1c_2}{a_1b_2-b_1a_2},\quad y=\frac{a_1c_2-c_1a_2}{a_1b_2-b_1a_2}$$
Solve two independent linear equations for two unknowns.
High schoolKeep going with algebra
A formula sheet is a reference, not a method. Use the subject guide to see where these relationships come from, a calculator to check a substitution you are unsure about, and practice questions to find out whether you can actually retrieve them.
- Study algebra — the subject hub with lessons, worked methods, and common mistakes.
- Algebra calculator — enter your own values and compare the result with your working.
- Algebra I Practice — retrieval practice across every topic listed above.
- Math formula library — search all 215 formulas by name, symbol, or condition.
Formulas in the other subjects
Mathematics does not stop at a subject boundary, and neither do its formulas. Each subject page below lists its own relationships, conditions, and worked examples.
Arithmetic
Review the core arithmetic relationships, their restrictions, and worked substitutions.
Geometry
Review the core geometry relationships, their restrictions, and worked substitutions.
Trigonometry
Review the core trigonometry relationships, their restrictions, and worked substitutions.
Precalculus
Review the core precalculus relationships, their restrictions, and worked substitutions.
Calculus
Review the core calculus relationships, their restrictions, and worked substitutions.
Statistics
Review the core statistics relationships, their restrictions, and worked substitutions.
Probability
Review the core probability relationships, their restrictions, and worked substitutions.
Linear Algebra
Review the core linear algebra relationships, their restrictions, and worked substitutions.
Differential Equations
Review the core differential equations relationships, their restrictions, and worked substitutions.
Discrete Math
Review the core discrete math relationships, their restrictions, and worked substitutions.