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Scientific Calculator
Type a whole expression instead of pressing keys one by one. Brackets, powers, percentages, factorials, constants and the usual scientific functions are supported, in degrees or radians.
How the expression is read
The calculator reads your text with a recursive-descent parser, which is a small set of rules that call each other. It never uses eval, so only the symbols listed below can run. Operators are applied in the standard order, from tightest binding to loosest:
- Brackets and function calls.
- Factorial
!and percent%, written after a value. - Powers
^, which group from the right, so2^3^2means2^(3^2) = 512. - Unary minus, so
-2^2is-4while(-2)^2is4. - Multiplication and division, left to right.
- Addition and subtraction, left to right.
Implicit multiplication is deliberately not guessed: write 2*pi, not 2pi, and 3*(4+1), not 3(4+1). A clear message tells you where an operator is missing.
Functions, constants and angle mode
| Name | Meaning |
|---|---|
| sin, cos, tan | Trigonometric functions; the input follows the angle mode |
| asin, acos, atan | Inverse trigonometric functions; the output follows the angle mode |
| sinh, cosh, tanh | Hyperbolic functions (no angle conversion) |
| ln, log, log2 | Natural log, base-10 log, base-2 log |
| sqrt, cbrt | Square root and cube root (cbrt accepts negatives) |
| abs, exp | Absolute value and e raised to a power |
| floor, ceil, round | Round down, up, or to the nearest whole number with halves moving away from zero |
The constants are pi (3.14159...) and e (2.71828...). In degree mode, angles that are exact multiples of 90 return exact values, so sin(180) is 0 and not a tiny rounding residue.
What the percent and factorial symbols do
The % sign divides the value before it by 100. It is not a remainder (modulo) operator, and it does not adjust the other side of a sum the way some handheld calculators do. So 200*10% is 20, but 100+10% is 100.1. To add ten percent to 100, write 100*(1+10%).
A factorial multiplies all whole numbers from 1 up to the value, so 5! is 120. It is only defined here for whole numbers from 0 to 170, because 171! overflows the largest number that standard double-precision arithmetic can store.
Precision and limits
Calculations use standard 64-bit floating-point numbers, which carry about 15 to 17 significant digits. Results are shown to 12 significant digits to hide harmless rounding noise such as 0.1+0.2 producing 0.30000000000000004. Very large or very small answers switch to a power-of-ten display. For exact big-integer work use the factorial or prime tools instead of this one.
Domain errors are reported rather than hidden: dividing by zero, taking the square root of a negative number, the logarithm of zero or a negative number, and asin or acos of a value outside the range from -1 to 1 all return a message. A negative base raised to a fractional power has no real result, so use cbrt for cube roots of negatives.
Worked example
In degree mode the sine of 30, the cosine of 60 and the tangent of 45 are 0.5, 0.5 and 1, so the sum is 2.
Inputs
| Expression | sin(30) + cos(60) + tan(45) |
|---|---|
| Angle mode | Degrees |
Result
Evaluated in degrees mode.
| Expression as read | sin(30) + cos(60) + tan(45) |
|---|---|
| Result to 12 significant digits | 2 |
| Scientific notation | 2.000000e+0 |
Accuracy note: Results use standard double-precision arithmetic, so very large or very small values may be rounded. Check important results by another method.
Frequently asked questions
How do I switch between degrees and radians?
Use the angle mode selector. Degree mode converts the input of sin, cos and tan from degrees, and returns the output of asin, acos and atan in degrees. Radian mode uses raw radians.
Why does -2^2 give -4 and not 4?
The power operator binds tighter than the minus sign in front of it, so the calculator squares 2 first and then negates. Write (-2)^2 when you want the square of negative two.
Does the calculator use eval?
No. The text is split into tokens and evaluated by a hand-written parser that accepts only numbers, operators, brackets, two constants and a fixed list of functions, so nothing else can be executed.
What is the largest factorial I can compute?
You can compute up to 170!, which is about 7.26 × 10^306. A larger value exceeds the range of double-precision numbers. The factorial calculator on this site handles bigger values with exact integers.
Why does log(100) give 2 but ln(100) give 4.605?
The log function is base 10, so it asks which power of 10 gives 100. The ln function is the natural logarithm, base e, so it asks which power of e gives 100.
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References and sources
- IEEE 754 standard for floating-point arithmetic, which defines the 64-bit number format used in the calculation.
- NIST Digital Library of Mathematical Functions, a reference for the definitions of trigonometric, exponential and logarithmic functions. Link