sin(30) + sqrt(9)
DEG: ≈ 3.5
In degrees, sin(30) is one half and the square root of 9 is 3. In radians, the same typed expression gives a different answer. Check the unit before calculating.
Numbers
Scientific Calculator
Work with angles, logarithms, roots, and powers in one expression. Type with your keyboard or build your calculation using the keys below.
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Result
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Try these expressions
log(1000) + 5!
≈ 123
log is base ten, so log(1000) is 3. A factorial multiplies positive integers up to its argument: 5! = 5 × 4 × 3 × 2 × 1 = 120. The numeric evaluation may be marked approximate even when the mathematical answer is an integer.
2^3^2
512
Powers group from the right: 2^(3^2) = 2^9 = 512. To square eight instead, enter (2^3)^2, which gives 64. Parentheses make the intended grouping explicit.
Function and input guide
Trigonometry
sin(x), cos(x), and tan(x) use the selected angle unit. asin(x), acos(x), and atan(x) are inverse functions that return angles, not reciprocals. asin and acos require −1 ≤ x ≤ 1.
Inverse functions return their principal values: asin from −90° to 90°, acos from 0° to 180°, and atan strictly between −90° and 90°; RAD gives the corresponding radian ranges.
Roots and absolute value
sqrt(x) returns the nonnegative square root and requires x ≥ 0. cbrt(x) accepts negative values too: cbrt(-8) = −2. abs(x) returns the distance from zero.
This calculator uses real numbers. sqrt(-1) and a negative base raised to a noninteger power are rejected. Use cbrt for a negative real cube root.
Logarithms and exponentials
ln(x) is the natural logarithm; log(x) is base ten. Both require x > 0. exp(x) means ex. For another logarithm base, use ln(value) / ln(base), with a positive base other than 1.
pi or π is the circle constant. A standalone e is Euler's number. Both constants are evaluated numerically.
Numbers, powers, and postfix operators
1.2e6 or 1.2E6 means 1.2 × 106. The e immediately after a number introduces its exponent; use 2 * e to multiply by Euler's number. Grouped commas are accepted in numbers such as 1,234.5.
x^y raises x to y. n! accepts integers from 0 to 170, with 0! = 1. x% means x / 100 in every context.
Order, precision, and limits
Parentheses and function arguments group their contents first. Factorial and percent are postfix operators. Powers group from the right and take priority over a leading minus: -2^2 = −4, while (-2)^2 = 4. A negative exponent is allowed: 2^-3 = 0.125. Multiplication and division then evaluate from left to right, followed by addition and subtraction from left to right. Multiplication must always be written explicitly. Double factorial (!!) is not supported; to apply factorial twice, use parentheses, as in (3!)!.
Arithmetic and functions use 80 significant digits internally. The final display uses your selected 6, 10, 12, 15, or 20 significant figures, with nearest-value rounding and exact halfway cases away from zero. The ≈ marker indicates numerical evaluation or rounding; it is not an error estimate. Subtracting nearly equal large values can lose useful digits, and increasing the display setting cannot recover information already lost during evaluation.
Each expression may contain up to 512 characters, 256 tokens, and 32 levels of nesting. Each numeric literal accepts up to 30 mantissa digits and an entered e exponent from −1000 to 1000. Nonzero input values, intermediate values, and results must have an absolute value from 10−1000 through 101000. Zero itself is allowed. Power exponents must have absolute value at most 1000; trigonometric input angles must have absolute value at most 1,000,000 in the selected unit.
Division by zero, 0^0, and function arguments outside the real-number domain produce an explanation instead of a numeric result. Tangent is undefined at odd multiples of 90° in DEG. Numerical evaluation also rejects tangent when the absolute computed cosine is below 10−60, too close to an undefined angle for this calculator's precision. Use parentheses and simpler intermediate expressions to check a result near a limit.
For exact fraction arithmetic and side-by-side number formats, use the Scientific Notation Calculator. For a choice of rounding directions, use the Rounding Calculator. Read the calculation policy for the rules used by each tool.
References: OpenStax on angles and the unit circle, inverse trigonometric functions, and logarithms; decimal.js documentation for the numerical library. The input limits and display choices above are specific to this calculator.
Common questions
How is this different from the Scientific Notation Calculator?
This tool evaluates expressions with trigonometry, logarithms, roots, powers, and factorials. The Scientific Notation Calculator focuses on converting numbers and doing exact rational arithmetic with one or two inputs. It shows scientific notation, e notation, and the full decimal together. Both tools remain available.
Why does sin(30) not give 0.5?
Check the angle unit. In DEG, the input means 30 degrees. In RAD, it means 30 radians. Enter sin(pi / 6) in RAD for the same angle as 30 degrees.
Does asin mean one divided by sine?
No. asin is inverse sine: it returns the principal angle whose sine is the input. In DEG, asin(0.5) gives approximately 30. To calculate the reciprocal of sine instead, enter 1 / sin(angle), provided the sine is nonzero. acos and atan follow the same inverse-function convention.
Why does 200 + 10% give 200.1?
Percent always means divide by 100, so 10% becomes 0.1 before addition. To increase 200 by 10%, enter 200 * (1 + 10%). This matches the Standard Calculator and keeps percent behavior consistent across expressions.
Does choosing 20 figures guarantee 20 correct digits?
No. The choice controls display length. This is a finite-precision numerical calculator, and expressions with severe cancellation or sensitive function values can lose accuracy. The ≈ marker does not measure the size of that uncertainty. For a critical calculation, check the formulation and verify with an appropriate independent method.