Math tools cover common calculations such as percentages and arithmetic averages, showing both the result and the formula used.
Start with the problem, then choose the tool matching your known quantities. Each topic includes an illustrative example and links to the relevant calculators.
Use percentage for part of a total, change for old versus new, difference for symmetric comparison, and error against a reference. Different denominators give different results.
Quick example: Moving from 80 to 100 is a 25% increase; returning to 80 is a 20% decrease because the base changes.
Arithmetic mean fits equally weighted values; weighted mean allows different importance. Geometric mean suits positive growth factors; harmonic mean may suit rates over equal distances or quantities.
Quick example: Scores 80 and 100 with weights 1 and 3 give weighted mean 95, versus arithmetic mean 90.
Use prime factors for number structure and GCD/LCM for fractions and repeating cycles. Base conversion or Roman notation changes representation, not the value.
Quick example: For 12 and 18, the greatest common divisor is 6 and least common multiple 36.
Identify a quadratic equation, linear system or matrix operation. Check logarithm and root domains, and distinguish matrix multiplication from multiplying matching entries.
Quick example: Equation x²−5x+6=0 has roots 2 and 3; substituting either makes the left side zero.
A constant difference defines an arithmetic sequence; a constant factor defines a geometric one. Linear interpolation estimates between two points on a line, without proving all data follow a linear relationship.
Quick example: A sequence starting at 3 and adding 4 each time has fifth term 19.
Choose the shape and whether you need area or perimeter. Triangle area uses perpendicular height; distinguish circle radius from diameter. Area units are squared; perimeter units are lengths.
Quick example: A square of side 5 has perimeter 20 and area 25, in length and squared units respectively.
Use dimensions for the same solid in one length unit. Surface area covers faces; volume describes space. A cone’s perpendicular height differs from slant height.
Quick example: A cube of side 4 has volume 64 and surface area 96, in cubic and squared units.
Use slope for line direction, midpoint for segment centre, and distance for length. A vector has magnitude and direction; negative components indicate axis direction.
Quick example: Distance from (0, 0) to (3, 4) is 5 and midpoint (1.5, 2).
For counting, check whether order matters and repetition is allowed. A z-score measures distance from the mean; converting it to normal probability needs a suitable model assumption.
Quick example: Choosing two of five without order gives 10 combinations; with order gives 20 permutations.
Enter assessment weights or credit hours and choose the correct GPA scale. Percentage grades and grade points are different units; conversion requires a stated grading policy.
Quick example: Assessments 80 and 90 weighted 40% and 60% give final grade 86%.
Aspect ratio preserves image shape, average speed divides total distance by total time, and Ohm’s law connects voltage, current and resistance. Identify known quantities before solving.
Quick example: Distance 120 km in 3 hours gives average speed 40 km/h.
Work out percentages, averages, and other everyday math.
Find percent of a number, percentage changes, reverse percentages, increases and discounts with six free instant calculation modes.
x̄Calculate mean, median, mode, population and sample standard deviation, sum and range instantly from your data.
Δ%Calculate percentage increase or decrease and the absolute difference between an old and a new value.
a:bSimplify A:B and split totals, or solve any missing A, B, C or D in A:B = C:D with cross-multiplication and an equality check.
½Add, subtract, multiply or divide two fractions, automatically simplify the result, and see fraction, mixed-number and decimal forms.
∣Find the GCD and LCM of two or more positive integers using exact integer arithmetic and the Euclidean algorithm.
×10ⁿConvert numbers to scientific notation, E notation and engineering notation, with powers of ten, worked examples and basic arithmetic.
XIVConvert integers from 1 to 3999 to standard Roman numerals and back with strict format validation.
Δ÷avgCompare two values without treating either as the starting point, with absolute difference, reference average and symmetric percent difference.
x̄ Me MoAnalyze a list of numbers and get mean, median, mode, range, sum, count, minimum and maximum.
P(A)Calculate a simple event, two independent events, combinations and permutations, or binomial probability with explicit assumptions and limits.
ax²Solve ax²+bx+c=0 for real or complex roots and show the discriminant, root type, parabola vertex and axis of symmetry.
πr²Enter radius, diameter, circumference or area to derive all four core circle measurements from one known value.
a²+b²Find the hypotenuse or either leg of a right triangle, plus area, perimeter and acute angles with input validation.
%errCompare a measured value with an accepted reference and show absolute error, signed error and percent error, including the zero-reference case.
V=IRUse Ohm’s law V=IR and power formulas to calculate voltage, current, resistance or electrical power from any two known values, with common unit prefixes.
△Solve a triangle from SSS, SAS, ASA/AAS or SSA and return sides, angles, area, perimeter, inradius and circumradius.
Δy/ΔxFind slope, rise, run, angle, line equation, midpoint and distance from two points, with explicit handling for vertical lines.
16:9Find an aspect ratio from dimensions or solve a missing width or height while resizing, with simplified ratio, decimal ratio and orientation.
πr²hCalculate cylinder volume, base area, lateral area, total surface area and circumference from radius or diameter plus height.
Σxw/ΣwCalculate a weighted average from values and weights, with total weight, weighted sum, simple mean and an optional next value needed to hit a target.
▭Calculate rectangle area, perimeter and diagonal from length and width, or recover the two sides from a valid area-and-perimeter pair.
◯³Enter a radius or diameter to get sphere volume, surface area, great-circle circumference and great-circle area with correct unit powers.
2↔16Convert integers exactly between binary, octal, decimal and hexadecimal using arbitrary-precision integer arithmetic.
□Calculate the perimeter of a square from its side, area or diagonal. Also find area, side length and both circle radii with step-by-step formulas.
△³Calculate cone volume, total surface area, lateral area, base area and slant height from radius or diameter plus height or slant height.
d÷tSolve average speed, distance or time from the other two values, with km/h, mph and m/s equivalents and consistent distance units.
nPr/nCrCalculate exact nPr and nCr and compare repetition-allowed counts for whole-number inputs up to n and r = 1000 without floating-point rounding.
◫³Start from side length, volume, surface area or space diagonal and recover the cube’s main measurements with correct unit powers.
⏢Calculate trapezoid area from parallel bases and perpendicular height, solve for a missing height or base, and find perimeter when both legs are known.
▭³Calculate cuboid volume, total and lateral surface area, base area, space diagonal and edge length, or recover height from a known volume.
⬡Find area, perimeter, interior/exterior angles, apothem, circumradius and diagonal count from the side count and one known size.
GPACalculate term and cumulative GPA from course grade points and credits on a 4.0 or 5.0 scale, with an optional target-GPA planner.
zσCalculate z from a raw value, mean and standard deviation, recover a raw value from z, or convert a percentile to z with normal-tail probabilities.
aₙCalculate the nth term, sum of the first n terms, average and an initial term preview from the first term and common difference.
rⁿCalculate the nth term, finite sum and initial terms, plus the infinite sum when the common ratio has absolute value below 1.
MFind the midpoint between two points in 2D or 3D, together with coordinate differences and the half-displacement vector.
↔Calculate Euclidean distance between two 2D or 3D points, plus Manhattan and Chebyshev distances and coordinate deltas.
▦Add, subtract and multiply 2×2 or 3×3 matrices, and calculate determinant, transpose and inverse with operation validation.
logCalculate natural, common, binary or custom-base logarithms, plus the inverse exponent operation.
p×qFactor a positive integer into primes and show exponential form, distinct prime factors, divisor count and prime/composite status.
▱Solve a parallelogram from two side lengths and the included angle, calculating area, perimeter, height and both diagonals.
⬭Calculate ellipse area, approximate circumference, eccentricity and focal distance from the semi-major and semi-minor axes.
a+biAdd, subtract, multiply or divide two complex numbers and calculate modulus, argument, conjugate and polar form of the result.
A+Calculate a weighted course grade from multiple scores and weights, or find the final-exam score needed to reach a target.
n!Calculate n! exactly for non-negative integers up to 2000, with digit count and trailing-zero count.
modCalculate exact integer quotient and remainder, showing both programming-style remainder and Euclidean modulo for negative inputs.
ⁿ√Calculate real nth roots, including odd roots of negative numbers, with a power-back verification.
GMCalculate the geometric mean of positive values with a numerically stable log method, alongside the arithmetic mean and count.
HMCalculate the harmonic mean for positive rates or values, with geometric and arithmetic means for comparison.
◔Calculate sector area, arc length, chord, sector perimeter and circular-segment area from radius and angle in degrees or radians.
◇Calculate rhombus area, perimeter, height, side length and diagonals from the two diagonals or from a side and included angle.
↗Estimate y at a target x from two known points, with slope, interval position and an interpolation-versus-extrapolation flag.
△▭Calculate triangular-base area, volume, lateral area and total surface area from the three triangle sides and prism length using a stable Heron formula.
△□Calculate a right square pyramid’s volume, face slant height, lateral edge, lateral area and total surface area from base side and vertical height.
⌒Calculate cone-frustum volume, slant height, lateral area and total surface area from the two radii and perpendicular height.
Ax=bSolve 2-variable and 3-variable systems of linear equations with partial-pivot Gaussian elimination, including unique, no-solution and infinitely-many cases.
2π²Rr²Calculate torus volume, surface area, inner radius and outer radius from major radius R and tube radius r for ring or horn tori.
A·BCalculate two 3D vector magnitudes, dot product, cross product and its magnitude, plus the angle between nonzero vectors.
First identify the calculation you need, enter comparable values, then review the formula and example below the calculator.
Yes. The formula and examples can help you review the calculation steps.
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