Math Reference

Math Formula Library

Review the formulas used across Toolarithm's math tools, then open the matching calculator when you need live inputs, unit labels, copy actions, print-ready results, or method tables.

Open notation calculator Math calculators

Formula coverage

5 groups

Arithmetic, algebra, geometry, statistics, scientific notation, and number theory formulas connect directly to live tools.

Editorial formula diagram showing percentage, slope, circle area, and mean relationships from the math formula library. — A compact map of representative arithmetic, coordinate, geometry, and statistics formulas in the library.

Formula Tables

Core formulas with matching calculators

Core arithmetic

Formula	Rule	Tool
Percent of value	part = value x percent / 100	Open
Percent change	change % = (new - original) / original x 100	Open
Fraction addition	a/b + c/d = (ad + bc) / bd	Open
Ratio scale	new second = second x target first / first	Open

Algebra and coordinates

Formula	Rule	Tool
Linear equation	ax + b = c -> x = (c - b) / a	Open
Slope	m = (y2 - y1) / (x2 - x1)	Open
Midpoint	M = ((x1 + x2) / 2, (y1 + y2) / 2)	Open
Distance	d = sqrt((x2 - x1)^2 + (y2 - y1)^2)	Open

Geometry and trigonometry

Formula	Rule	Tool
Circle area	A = pi r^2	Open
Triangle area	A = base x height / 2	Open
Pythagorean theorem	a^2 + b^2 = c^2	Open
Radians	radians = degrees x pi / 180	Open

Statistics

Formula	Rule	Tool
Mean	mean = sum of values / n	Open
Sample variance	s^2 = sum((x - xbar)^2) / (n - 1)	Open
Percentile rank	rank = 1 + (n - 1) x p	Open
Z-score	z = (x - mean) / standard deviation	Open

Notation and number theory

Formula	Rule	Tool
Scientific notation	number = a x 10^n	Open
Prime factorization	n = p1^a x p2^b x ...	Open
GCD	use lowest shared prime powers	Open
LCM	use highest required prime powers	Open

How To Use

Move from formula reference to checked result

Choose the formula family

Start with the topic group that matches the problem: arithmetic, coordinate, geometry, statistics, or number theory.

Open the matching tool

Use the linked calculator when values, units, edge cases, or printable output matter.

Check method notes

Read the calculator's formula table and FAQ to confirm assumptions before using the answer.

Sources

Reference links used for formula checks

OpenStax Prealgebra: geometric formulas OpenStax Intermediate Algebra: slope OpenStax Prealgebra: scientific notation OpenStax Prealgebra: prime factorization

Day 12 math wrap-up

Scientific notation, factors, GCD, and LCM are live

Open GCD and LCM

Editorial Transparency

Who maintains this page

Ownership and review

Written and maintained by the Toolarithm editorial team. No review date is shown without a maintained editorial record. No independent professional review is claimed.

Methodology

The editorial team checks definitions, examples, linked tools, and cited references. Dates shown here come from the page's maintained publication record.

Read the editorial methodology

Dates and sources

Review dates change only after a substantive method or content check.