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Mathematics · pattern D, Mode switcher

The standard functions, one at a time and shown clearly.

Pick an operation and enter a value. The result arrives with the related quantities and the domain restriction that applies, rather than an error message you have to interpret.

Inputs

Operation

The formula used

each operation applied to a single value x

Deliberately not a keypad. Showing one operation with its domain and its related values is more useful for learning than a grid of buttons that hides the step.

Result

12.00000000

Square root; undefined for negative x in the reals.

Square root
12.00000000
Square
20,736.000000
Natural log
4.96981330
Log base 10
2.15836249
Exponential eˣ
3.455e+62
Reciprocal
0.00694444

Domains are where calculators go quiet.

Square roots of negatives, logs of zero and factorials of fractions are all undefined in the ordinary reals, and most calculators answer with a terse error. Knowing which operation carries which restriction is part of understanding the function, so this page states the domain rather than merely refusing.

Questions about scientific

What is the difference between ln and log?
ln is base e, about 2.718. log means base 10 in schools and base e in mathematics and code, so check the convention before trusting a result.
Why is 0! equal to 1?
Because there is exactly one way to arrange nothing, and because it keeps the recursive definition and the binomial coefficients consistent.
Can I take an even root of a negative number?
Not in the reals. Odd roots are fine — the cube root of −8 is −2.

More in Mathematics

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A calculator handles the arithmetic. It cannot teach you the method.

If the number is not the part you are stuck on, that is what the service is for — a specialist who explains the working, not just the answer.

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Arithmetic runs in double-precision floating point, so results beyond about fifteen significant figures are not exact. Where a question wants an exact fraction or surd, keep the exact form rather than a decimal.