Math Calculators
Free calculators for everyday math and school math, from percentages and averages to roots, triangles and matrices. Many of them show the working step by step.
34 calculators each one also works as a widget
Percentages and ratios
6- Percentage Calculator Percent of a number, what percent, percent change and a percent of a percent, with steps.
- Percent Error Calculator Percent error between a measured and a true value, for one or several trials.
- Proportion Calculator Solve a proportion by cross multiplication, scale a recipe or compare ratios.
- Unit Rate Calculator Find the unit rate or unit price and compare offers to find the best deal.
- Rate of Change Calculator Average rate of change between two points or over an interval of a function.
- Golden Ratio Calculator Splits a length in the golden ratio, sizes a golden rectangle, checks a ratio against φ or builds a type scale.
Averages and statistics
6- Average Calculator Find the mean of any list of numbers, with the median, mode, range and sum.
- Weighted Average Calculator Average values that count for different amounts, such as weighted grades.
- Standard Deviation Calculator Sample or population standard deviation, with the variance and the mean.
- Geometric Mean Calculator Finds the geometric mean of positive numbers, the average of growth rates and CAGR, with steps and exact roots.
- Harmonic Mean Calculator Harmonic mean of a list of numbers, the right average for rates such as speeds.
- Linear Interpolation Calculator Find a value between two known points or in a table, or the x for a given y.
Arithmetic and fractions
8- Mixed Number Calculator Add, subtract, multiply or divide mixed numbers, or convert them to improper fractions and decimals, with steps.
- Long Division Remainder Calculator Long division of two numbers with every step, giving the quotient and remainder or a decimal.
- Modulo Calculator Find a mod n with steps, for negative numbers and whole numbers of any size.
- Rounding Calculator Round a number to any decimal place or to the nearest multiple.
- GCD Calculator Greatest common factor (GCD or HCF) of two or more numbers, with the LCM and the steps four ways.
- LCM Calculator Least common multiple of two or more numbers, or the least common denominator of fractions, with steps.
- Factorial Calculator Find n! exactly with every digit, plus double factorials, subfactorials and factorials of fractions.
- Binary Calculator Add, subtract, multiply and divide binary numbers, or apply AND, OR, XOR and shifts, with the working in columns.
Powers, roots and logarithms
4- Exponent Calculator Raise any number to any power, including negative and fractional exponents, and get the exact answer with steps.
- Nth Root Calculator Square, cube or any nth root of a number, in simplest radical form with its decimal and all n roots.
- Radical Calculator Simplify square roots and other radicals by prime factorization.
- Logarithm Calculator The log of a number in any base, including ln and log base 10, or the antilog.
Geometry and trigonometry
6- Pythagorean Theorem Calculator Find any side of a right triangle with a² + b² = c².
- Law of Cosines Calculator Solve a triangle with the law of cosines: the third side (SAS), the angles (SSS) or the ambiguous SSA case.
- Orthocenter Calculator Find the orthocenter of a triangle from the coordinates of its three corners.
- Cylinder Volume & Area Calculator Volume of a cylinder in terms of π, litres and gallons, with its surface area, hollow cylinders and tank levels.
- Coterminal Angle Calculator Find coterminal angles in degrees or radians, the angle between 0° and 360°, the reference angle and the quadrant.
- Inverse Tangent Calculator The angle whose tangent is x (arctan), from a value, two sides or a point, in degrees and radians.
Algebra, sequences and matrices
4- Arithmetic Sequence Calculator Find any term, the nth term formula, the common difference and the sum of an arithmetic sequence.
- Matrix Calculator Multiply, add or subtract matrices and find the determinant, inverse, transpose, power, rank or RREF, with steps.
- Diagonalize Matrix Calculator Find the eigenvalues and eigenvectors of a square matrix and write it as A = PDP⁻¹, or see why it cannot be done.
- Cross Product Calculator Cross product of two vectors in i, j, k or bracket form, with steps, its length and the plane through three points.
Which Math Calculator Do You Need?
Start from the question you are trying to answer. If it has the word percent in it, the Percentage Calculator covers the usual forms: a percent of a number, what percent one number is of another, and percent change. For a list of test scores or measurements, the Average Calculator gives the mean with the median and range, and the Standard Deviation Calculator tells you how spread out the numbers are.
Use the Weighted Average Calculator when some values count more than others, such as a final exam worth half the grade. The geometric mean is the right average for growth rates, and the harmonic mean is the right one for rates such as speeds over equal distances.
Fractions, Remainders and Whole Numbers
The Mixed Number Calculator adds, subtracts, multiplies and divides fractions and mixed numbers and shows the steps. For division with whole numbers, the Long Division Remainder Calculator gives the quotient and what is left over. The Modulo Calculator gives the remainder the way programming languages do, including for negative numbers.
GCD and LCM are the two tools for fractions. The greatest common divisor (also called GCF or HCF) is the largest number that divides all of your numbers, so it simplifies a fraction. The least common multiple is the smallest number they all divide into, so it gives a common denominator.
Geometry, Trigonometry and Algebra
For triangles, use the Pythagorean Theorem Calculator when there is a right angle and the Law of Cosines Calculator when there is not. The Orthocenter Calculator works from the coordinates of the corners. Angle questions in degrees or radians go to the Coterminal Angle and Inverse Tangent calculators.
For linear algebra, the Matrix Calculator adds and multiplies matrices and finds the determinant, the Diagonalize Matrix Calculator finds eigenvalues and eigenvectors, and the Cross Product Calculator works with vectors in 3D.
Checking Your Own Work
A calculator helps most after you have tried the problem yourself. Work it out on paper first, then compare. Where a calculator shows its steps, read them line by line to find the place where your answer went a different way.
Watch the small print of the question as well. Rounding to two decimal places, giving an angle in degrees instead of radians, or using a sample instead of a whole population all change the answer, and the calculators let you choose each of these.
Frequently Asked Questions
Do the math calculators show the steps?
Many of them do, including the percentage, modulo, mixed number, factorial, radical and proportion calculators. Every calculator page also explains the formula with a worked example, so you can follow the method.
What is the difference between the mean and the median?
The mean is what most people call the average: add the numbers and divide by how many there are. The median is the middle number once the list is sorted. They differ when a few values are much larger or smaller than the rest. The Average Calculator shows both.
Which calculator should I use for a percent increase?
Use the Percentage Calculator. Enter the old and the new value in the percent change row, and it shows the increase or decrease along with the working.