Math Calculators
These 12 math calculators cover averages, fractions, ratios, percentages, matrices and statistics. Every one shows the formula it applied and defines each term, so you can check the working rather than trust the number.
12 tools
- Average CalculatorThis average calculator reports the mean, median, mode and range of a list of numbers, with both standard deviations, so you can see which average fits.
- Combination CalculatorThe combination calculator works out nCr and nPr side by side, with and without repetition, so the gap between a combination and a permutation is visible.
- Equation SolverThe equation solver handles ax2 + bx + c = 0, showing the discriminant, the vertex and both roots, including the complex pair when the discriminant is negative.
- Fraction CalculatorThe fraction calculator adds, subtracts, multiplies and divides fractions, simplifying the result and showing it as an improper fraction and a mixed number.
- List Sum CalculatorThe list sum calculator adds a column of numbers pasted in any format, reporting positive and negative subtotals separately alongside the count and the mean.
- Matrix Row ReducerRow-reduce a matrix to reduced row echelon form, with the rank and every elimination step shown.
- Percentage CalculatorThe percentage calculator covers five separate questions, including the difference between a change in percent and a change in percentage points, which differ.
- Ratio CalculatorThe ratio calculator simplifies a ratio of any number of parts, shows each part as a percentage of the whole, and scales the set to a new total you choose.
- Scientific CalculatorA scientific calculator with trigonometry, logarithms, powers and brackets, evaluated by a real expression parser rather than eval, so precedence is correct.
- Set Builder Notation ConverterTurn a list of numbers into set-builder notation, detecting an arithmetic pattern where one exists.
- T-Score CalculatorThe T score calculator converts a z-score or a raw value onto the mean-50, standard-deviation-10 scale used across psychometric and educational testing.
- Z-Score CalculatorThe z score calculator converts a raw value into standard deviations from the mean, and gives the matching percentile under the normal distribution curve.
What these math calculators cover
Four handle everyday arithmetic on sets of numbers: the average calculator reporting mean, median, mode and range, the list sum calculator for a pasted column, the percentage calculator covering five distinct percentage questions, and the ratio calculator for simplifying and scaling parts.
Four handle algebra and notation. The scientific calculator evaluates expressions through a real parser rather than eval, so operator precedence is correct and an input cannot execute code. The equation solver handles quadratics with the discriminant, vertex and both roots shown, including the complex pair. The fraction calculator returns a simplified result and a mixed number. The set builder notation tool translates between notation and plain English.
Three handle statistics: z-scores, T-scores on the mean-50 scale used in psychometric testing, and combinations and permutations side by side, with and without repetition, so the difference between the two is visible rather than assumed.
The matrix row reducer is the one that shows its work most fully. It lists every row operation performed, numbered, with the matrix redrawn after each one, because the sequence is the part a student needs rather than the final answer.
Which calculator for which question
Three of these can act on the same list of numbers and answer different questions about it.
| The question | The calculator |
|---|---|
| What is the typical value in this set | Average calculator, giving mean, median and mode together |
| How spread out is this set | Average calculator, reporting both sample and population standard deviation |
| What do these numbers add up to | List sum calculator, with positive and negative subtotals separated |
| How unusual is one value in a set | Z-score calculator, with the matching percentile |
| How many ways can these be arranged | Combination calculator, showing nCr and nPr side by side |
| Solve for x in a quadratic | Equation solver, including the complex roots when the discriminant is negative |
Frequently asked questions
Does the average calculator use the sample or population standard deviation?
Both, side by side. The sample figure divides by n minus 1 and the population figure divides by n. Statistics software normally defaults to the sample figure, and on a small set the two differ enough to change a conclusion, so the tool shows them together rather than picking.
Why does the scientific calculator not use the browser eval function?
Because eval would execute whatever you typed as JavaScript, which is both a security problem and a correctness one. The calculator tokenises the expression and evaluates it with a real precedence table, so multiplication binds tighter than addition and a stray character is reported rather than run.
What is the difference between a combination and a permutation?
Order. A combination counts selections where order does not matter, so picking A then B is the same result as B then A. A permutation counts arrangements where it does, making them two different results. The calculator shows nCr and nPr together for the same inputs so the gap is visible.
Can the equation solver handle cubic equations?
No. It covers degree two and the degenerate linear case where the leading coefficient is zero. Cubic and higher equations need either a numeric method or a symbolic solver, both of which are a different tool rather than an extension of this one.
Why does a percentage increase then decrease not return to the start?
Because each step is taken on a different base. A 50 percent rise from 100 gives 150, and a 50 percent fall from 150 gives 75, not 100. The second percentage applies to the larger figure. The percentage calculator shows the base it used at each step for exactly this reason.