Math Library

A keyboard-friendly scratch calculator for quick totals, percentages, ratios, per-unit costs, and order-of-operations checks while you work in the browser.

Calculate percent-of values, percent change, percent difference, and reverse percentages with visible formulas for discounts, markups, before-and-after values, and original-price reconstruction.

Calculate the percent increase from a start value to a final value, with the increase amount shown as the bridge between the two numbers.

Compare two measurements with symmetric percent difference, using the absolute gap divided by the average magnitude so neither value is treated as the original.

Calculate the final value after a percentage decrease by separating the original baseline, the amount removed, and the remaining value.

Back out the original value when you know the final value and the percentage increase or decrease that produced it.

Calculate the true sale price from a list price by applying the markdown first, then adding tax only to the discounted subtotal.

Compare a measured value with an accepted reference value by making absolute error visible first, then converting that error into a relative percentage.

Add, subtract, multiply, and divide fractions exactly, without decimal rounding, then read the simplified final result.

Simplify fractions into lowest terms by finding the GCD of the numerator and denominator, preserving the equivalent value, and normalizing signs.

Convert mixed numbers into improper fractions for exact arithmetic, then reduce and return the answer as a simplified fraction or mixed number.

Convert a decimal into the cleanest reduced fraction that fits a chosen denominator limit, showing when the result is exact and when it is an approximation.

Convert a fraction by treating the fraction bar as division, then check the reduced denominator to know whether the decimal ends or repeats.

Simplify a two-part ratio by finding the greatest common divisor, dividing both sides together, and keeping the comparison meaningful.

Solve equations in standard form ax^2 + bx + c = 0 by checking the discriminant first, then reading the real, repeated, complex, or linear result.

Solve a one-variable equation in the form ax + b = c by isolating x with two inverse moves, then checking special zero-coefficient cases.

Solve a 2x2 system by reading it as two lines, using the determinant to identify one intersection, no solution, or infinitely many solutions.

Calculate slope as rise over run between two ordered coordinate points, with clear handling for positive, negative, zero, and undefined slope cases.

Find the center of a line segment by averaging matching coordinates, x with x and y with y, regardless of which endpoint is entered first.

Find the straight-line distance between two coordinate points by turning delta x and delta y into the legs of a right triangle.

Find a missing side of a right triangle by identifying the hypotenuse first, then solving for a leg or the hypotenuse.

Find triangle area from a chosen base and its matching perpendicular height, with square units and no slanted-side shortcuts.

Calculate circle measurements from radius, showing how diameter and circumference grow linearly while area grows by the square.

Calculate cylinder volume as circular base area times height, while keeping cubic volume units separate from square surface units.

Calculate sphere volume and surface area from radius, with diameter-to-radius conversion, cubic-unit output, and radius growth checks.

Calculate cone volume as one third of the matching cylinder with the same circular base radius and vertical height.

Calculate mean, median, mode, and range from the same data set, then compare what each summary actually tells you.

Measure how tightly a data list clusters around its mean, compare population and sample standard deviation, inspect variance, and understand outlier-driven spread.

Calculate a weighted average from values and weights, with examples for grades, credits, portfolio allocations, zero-weight rows, and signed weights.

Calculate tip, tax, service charges, and per-person shares for a shared restaurant bill.