Statistics mode
Switch to the Statistics tab to compute descriptive statistics from a list of values. Paste numbers from a spreadsheet or type them manually, separated by commas, spaces, or new lines.
The panel calculates:
- Count, Sum, Mean, Median — core summary measures.
- Min, Max, Range — the spread of your data.
- Population standard deviation (σ) and variance (σ²) — when your list is the entire population.
- Sample standard deviation (s) and variance (s²) — when your list is a sample (uses n−1 in the denominator; requires at least 2 values).
Click Use beside any result to insert it into the main calculator — useful for chaining a standard deviation into a further expression.
Scope: This is a numeric descriptive-statistics tool. It does not perform hypothesis tests, confidence intervals, regression, or inference. Results are rounded by the current display precision.
Fractions mode
The Fractions tab has two tools:
- Fraction arithmetic — enter any two fractions (numerator and denominator separately) and choose + − × ÷. The result is shown fully reduced and as a decimal. Mixed-number notation is used for improper fractions (e.g. 7/4 → 1 3/4).
- Decimal → Fraction — enter a decimal (like 0.333 or 0.142857) to find the nearest fraction with a denominator of 1,000 or less. Useful for recognising recurring decimals and confirming division results.
All fractions are reduced to lowest terms using the greatest common divisor. Click Use decimal in calculator to continue with a result in the main expression.
Physical constants
The Constants tab provides quick access to 15 physical and mathematical constants from the NIST CODATA 2018 database. Search by name, symbol, or category (Math, Physics, Chemistry).
Available constants include π, e, the golden ratio φ, speed of light c, gravitational acceleration g, Planck constant h, Avogadro number Nₐ, Boltzmann constant k_B, elementary charge q, gas constant R, Stefan-Boltzmann constant σ, gravitational constant G, proton mass mₚ, electron mass mₑ, and the fine-structure constant α.
Click Use to insert any constant value into the current expression, then switch to the Scientific or Basic tab to continue.
Note: Only numeric magnitudes are inserted. Unit tracking is not performed — maintain consistent units in your calculations.
Worked examples
Each of these evaluates live in the calculator above — tap an example chip to load it. They show how the engine handles angles, logarithms, powers, factorials, percentages, implicit multiplication, and scientific notation.
Worked example expressions and results| Expression | Result | What it shows |
|---|
sin(30) | 0.5 | Trigonometry in degrees — the sine of a 30° angle. Switch to RAD and you would type sin(π/6). |
log(1000) | 3 | The base-10 logarithm: 10³ = 1000. Use ln for the natural (base-e) logarithm. |
2^10 | 1024 | A power: two to the tenth. The xʸ key inserts ^; x² is a one-tap shortcut for squaring. |
5! | 120 | A factorial: 5 × 4 × 3 × 2 × 1. Defined only for whole numbers from 0 upward. |
200 + 10% | 220 | Contextual percent — 10% of 200 is added. On its own, 10% would simply be 0.1. |
Common functions explained
A quick reference to the functions you will use most. Every one has an on-screen button and evaluates live in the calculator above.
Degrees vs radians (DEG / RAD)
Degrees split a circle into 360 parts; radians use the arc length of a unit circle, so a full circle is 2π. Use DEG for everyday geometry and RAD for calculus and physics. The active unit is shown in the badge above every result, and inverse trig functions return their answer in the same unit — so if sin(30) does not read 0.5, check whether you are in RAD (where you would enter sin(π/6) instead).
How percentages are interpreted
A standalone percentage is just a fraction: 50% = 0.5. In addition and subtraction it becomes a percentage of the left-hand value — 200 + 10% = 220 and 200 − 10% = 180 — which matches how shops and most pocket calculators apply discounts and markups. With × or ÷ it stays a plain fraction.
Common input errors
When an expression cannot be evaluated, the calculator shows a short, plain-language message in the result area (and announces it to screen readers) instead of returning a wrong number. The usual cases:
Common input errors and how to fix them| If you… | What you will see | How to fix it |
|---|
| Leave a bracket unclosed | "Missing a closing parenthesis" | Close every "(" with a ")". The ( ) key inserts whichever bracket fits next. |
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| Divide by zero | "Cannot divide by zero" | Check the denominator — dividing by zero has no defined value. |
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| Take a factorial of a decimal or negative | "Factorial needs a whole number" | n! works only for whole numbers of 0 or more. Use 5!, not 5.5! or (−3)!. |
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| Take a log or √ of 0 or a negative | "A logarithm needs a value greater than 0" | log, ln and log2 need a value above 0; √ needs 0 or more. |
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| Confuse DEG and RAD | A correct value for the wrong unit — no error | If sin(30) isn't 0.5, check the unit badge — you may be in RAD. Switch to DEG, or enter sin(π/6). |
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| Expect exact very-long decimals | A rounded value, sometimes in ×10ⁿ form | Results round for display; choose a fixed 2–8 decimals, or see Limitations below. |
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Sources & method
Method. Every result is computed in your browser by a hand-rolled expression engine (tokeniser → parser → evaluator) with no third-party math library, validated against hand-checked cases on every change. See Limitations for precision and rounding details.