➕ Mathematics

➕

Basic Math

Perform common addition, subtraction, multiplication and division calculations with two numbers. Includes the selected operation and a clear worked result.

%

Percentage

Calculate a percentage of a number, find what percentage one number is of another, and find the whole when a percentage and part are known.

📈

Percentage Change

Calculate the percentage change from an original value to a new value, including the signed increase or decrease.

↔️

Percentage Difference

Compare two values using percentage difference based on the average of their magnitudes.

⚠️

Percentage Error

Calculate percentage error by comparing an experimental or measured value with a reference or accepted value.

⚖️

Ratio

Simplify a two-part ratio, calculate decimal and percentage shares, and divide a total according to the ratio.

⚖️

Proportion

Solve a direct proportion a:b = c:d by calculating the missing fourth value from three known values.

x̄

Average

Calculate the arithmetic mean of two numbers and show their sum and count.

⚖️

Weighted Average

Calculate a weighted average from two values and their weights, useful when the values contribute unequally.

↔️

Midpoint

Find the midpoint between two numbers using the arithmetic mean of the two endpoints.

|x|

Absolute Value

Find the absolute value of a number, which represents its non-negative distance from zero.

1/x

Reciprocal

Calculate the reciprocal of a number by finding its multiplicative inverse.

÷R

Remainder

Calculate the quotient and remainder when one number is divided by another.

mod

Modulo

Calculate the mathematical modulo of one number by another using the floor-based definition.

≈

Rounding

Round a number to the nearest integer and compare it with its floor and ceiling values.

10ˣ

Scientific Notation

Convert a number into scientific notation by calculating its coefficient and power of ten.

⌊x⌋

Floor

Find the floor of a number, the greatest integer less than or equal to the input.

⌈x⌉

Ceiling

Find the ceiling of a number, the smallest integer greater than or equal to the input.

0.00

Decimal Places

Count how many decimal places a number has and round it to any number of decimal places, with a table of rounded, rounded-down and rounded-up values.

sig

Significant Figures

Count the significant figures in a number — including tricky zeros — and round it to any number of significant figures, with the answer in scientific notation.

➗

Fraction Calculator

Add, subtract, multiply or divide fractions and mixed numbers. The answer is reduced to lowest terms and shown as a fraction, a mixed number and a decimal.

½

Fraction Addition

Add two fractions and see the numerator, denominator and decimal result. Uses cross multiplication so unlike denominators can be handled.

✂️

Simplify Fraction

Reduce any fraction to its lowest terms and see the greatest common divisor used, the mixed-number form and the decimal value.

½

Fraction Subtraction

Subtract one fraction from another and calculate the exact numerator, denominator and decimal result.

½

Fraction Multiplication

Multiply two fractions and calculate the numerator, denominator and decimal result.

½

Fraction Division

Divide one fraction by another using the reciprocal rule and calculate the decimal result.

½

Fraction to Decimal

Convert a fraction to its decimal value.

½

Fraction to Percentage

Convert a fraction into a percentage.

½

Fraction of a Number

Calculate what fraction of a number represents.

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Compare Fractions

Compare two fractions using cross multiplication and show the larger value.

½

Fraction Reciprocal

Find the reciprocal of a fraction and its decimal value.

½

Mixed to Improper

Convert a mixed number into an improper fraction.

½

Improper to Mixed

Convert an improper fraction into whole-number and remainder parts.

½

Decimal to Fraction

Convert a terminating decimal to a fraction using a user-selected number of decimal places.

½

Fraction to Ratio

Express a fraction as a two-part ratio using its numerator and denominator.

½

Fraction of Whole

Find what percentage of a whole a numerator represents when the total is known.

^

Power

Calculate a number raised to an exponent.

²

Square

Calculate the square of a number.

³

Cube

Calculate the cube of a number.

√

Square Root

Find the principal square root of a non-negative number.

∛

Cube Root

Find the real cube root of a number.

ⁿ√

Nth Root

Calculate the principal real nth root of a positive number.

log

Logarithm

Calculate a logarithm with a custom base.

ln

Natural Log

Calculate the natural logarithm of a positive number.

log10

Log Base 10

Calculate the common logarithm, base 10.

log2

Log Base 2

Calculate the base-2 logarithm.

📈

Exponential Growth

Calculate repeated percentage growth.

📉

Exponential Decay

Calculate repeated percentage decay.

10x

Power of 10

Calculate 10 raised to any exponent.

2x

Doubling Time

Find how long anything growing at a steady rate takes to double, using the doubling time formula Td = ln 2 ÷ ln(1 + r). Includes the rule of 70 and 72, continuous growth and the biology formula.

＝

Linear Equation

Solve a linear equation of the form ax + b = c for x.

x

Two-Step Equation

Solve equations of the form a(x + b) = c for x.

↗

Line Equation

Find the slope and y-intercept of a line passing through two points.

m

Slope

Calculate the slope of a line from two points.

b

Y-Intercept

Find the y-intercept when the slope and one point on a line are known.

y=

Line Equation

Find the slope-intercept equation of a line from its slope and one point.

Δ

Discriminant

Calculate the discriminant of ax^2 + bx + c = 0 and identify the root type.

x²

Quadratic Roots

Solve ax² + bx + c = 0 and calculate the real or complex root components.

V

Vertex

Find the vertex and axis of symmetry of a quadratic y = ax² + bx + c.

x=

Axis of Symmetry

Calculate the axis of symmetry of a quadratic y = ax² + bx + c.

P(x)

Polynomial Value

Evaluate a quadratic polynomial ax² + bx + c at a chosen x value.

min/max

Min / Max

Find the minimum or maximum value of a quadratic y = ax² + bx + c.

y=kx

Direct Variation

Find the constant of variation and calculate y for a direct variation y = kx.

y=k/x

Inverse Variation

Find the constant of inverse variation and calculate y for a new x.

x%

Percentage Equation

Find the unknown amount when a percentage relationship is known.

➕

Quadratic Roots

Solve ax²+bx+c=0 for real roots (discriminant ≥ 0).

🔢

Divisibility

Check whether one integer divides another exactly and see the quotient and remainder.

➗

Quotient & Remainder

Calculate the integer quotient and remainder when dividing one whole number by another.

2️⃣

Even or Odd

Determine whether a whole number is even or odd using its remainder after division by 2.

✖️

Multiple Checker

Check whether one whole number is an exact multiple of another and calculate the multiple when applicable.

🔗

Common Divisor

Check whether a chosen integer is a common divisor of two numbers.

◻️

Perfect Square

Check whether a positive integer is a perfect square and calculate its nearest integer square root.

🧊

Perfect Cube

Check whether a number is a perfect cube and calculate its nearest integer cube root.

🔟

Number of Digits

Count the number of decimal digits in a positive whole number.

xʸ

Power / Exponent

Calculate a power and check a selected exponent relationship.

🔄

Digital Root

Calculate the digital root of a positive integer using repeated modulo-9 arithmetic.

🧮

Modular Arithmetic

Calculate the remainder of an integer after division by a positive modulus.

🔗

Divisor / Multiple

Determine the quotient, remainder and exact-multiple relationship between two whole numbers.

2ⁿ

Power of 2

Check whether a positive integer is an exact power of two and estimate its logarithm base 2.

▭

Rectangle Area

Calculate the area of a rectangle from its length and width.

▭

Rectangle Perimeter

Calculate the perimeter of a rectangle from its length and width.

▭

Rectangle Diagonal

Calculate the diagonal of a rectangle using the Pythagorean relationship.

□

Square

Calculate the area, perimeter and diagonal of a square.

▱

Parallelogram Area

Calculate the area of a parallelogram from its base and perpendicular height.

▱

Parallelogram Perimeter

Calculate the perimeter of a parallelogram from its two side lengths.

▰

Trapezoid Area

Calculate the area of a trapezoid from its two parallel sides and height.

◇

Rhombus Area

Calculate the area of a rhombus from its diagonals.

◇

Rhombus Perimeter

Calculate the perimeter of a rhombus from its side length.

◇

Kite Area

Calculate the area of a kite from its diagonals.

○

Circle Area

Calculate the area of a circle from its radius.

○

Circle Circumference

Calculate the circumference of a circle from its radius.

○

Circle Diameter

Calculate the diameter of a circle from its radius.

◉

Annulus Area

Calculate the area of an annulus or ring from its outer and inner radii.

⬭

Ellipse Area

Calculate the area of an ellipse from its semi-major and semi-minor axes.

▣

Cuboid Volume

Calculate the volume and surface area of a cuboid.

⬛

Cube Volume

Calculate the volume and surface area of a cube.

◯

Cylinder Volume

Calculate the volume and total surface area of a cylinder.

△

Cone Volume

Calculate the volume, slant height and total surface area of a right circular cone.

●

Sphere

Calculate the volume, surface area and diameter of a sphere.

◐

Hemisphere

Calculate hemisphere volume and surface areas from its radius.

🔺

Triangle Area

Calculate the area of any triangle when its base and perpendicular height are known. Includes the standard triangle area formula, worked example, units and key triangle terminology.

📐

Heron's Formula

Calculate triangle area from all three side lengths using Heron's formula. Check the triangle inequality and find the semiperimeter and area from three sides.

📐

Right Triangle Area

Calculate the area of a right triangle from its two perpendicular legs. The calculator also finds the hypotenuse using the Pythagorean theorem.

🔺

Equilateral Triangle

Calculate the area, height, perimeter, inradius and circumradius of an equilateral triangle from its side length.

🔺

Isosceles Triangle

Calculate the area and height of an isosceles triangle from its two equal sides and base. Includes triangle validity checking and a worked example.

📍

Coordinate Triangle Area

Calculate the area of a triangle from the x and y coordinates of its three vertices using the coordinate or shoelace formula.

⭕

Inradius Area

Calculate triangle area from its inradius and semiperimeter using the standard area relationship A = r × s.

⭕

Circumradius Area

Calculate the area of a triangle from its three side lengths and circumradius using A = abc divided by 4R.

📏

Median Area

Calculate triangle area when one side, the adjacent side and the median to the known base are given. Uses the median geometry and Pythagorean relationship.

🔺

30-60-90 Triangle

Calculate the area and all three side lengths of a 30-60-90 special right triangle from its short leg.

📏

2D Distance

Calculate the straight-line distance between two points on a Cartesian plane.

÷

Section Formula

Find the internal division point of a line segment in a given ratio.

━

Line From 2 Points

Find the slope and y-intercept of the line through two non-vertical points.

│

Vertical Line

Find the equation of a vertical line through a given x-coordinate.

─

Horizontal Line

Find the equation of a horizontal line through a given y-coordinate.

X

X-Intercept

Find the x-intercept of a line in slope-intercept form.

f(x)

Line Value

Calculate y for a line y = mx + b at a chosen x-value.

∥

Parallel Line

Find the equation of a line parallel to a given slope through a point.

⊥

Perpendicular Line

Find the equation of a line perpendicular to a given nonzero slope through a point.

📐

3D Distance

Calculate the straight-line distance between two points in three-dimensional Cartesian space.

◉

3D Midpoint

Find the midpoint of a line segment between two points in three-dimensional space.

△

Centroid

Find the centroid coordinates of a triangle from its three vertex coordinates.