Why does square root of a negative number show an error?

In real-number mathematics, the square root of a negative number is undefined because no real number squared produces a negative value.

What is the difference between log10 and ln?

log10(x) uses base 10 (common log), whereas ln(x) uses base e ≈ 2.71828 (natural log used in calculus and physics).

How do I convert degrees to radians?

Multiply the angle in degrees by π / 180 (~0.0174533).

Scientific Calculator

Select a mathematical function (exponents, roots, logs, trigonometry, factorials) and enter your values to compute exact scientific results and notation.

How to use this calculator

Select your desired mathematical function from the dropdown list.
Enter the value for x (and exponent y if calculating powers).
If calculating trigonometric functions (sin, cos, tan), select Degrees or Radians.
Read your result in standard decimal, scientific notation, x squared, and x cubed formats.

Formula & method

Standard Scientific & Transcendental Functions

Power: x^y · Sqrt: √x · Log10: log10(x) · Ln: ln(x) · Sin: sin(rad) · Factorial: x! = 1×2×...×x

rad = deg × (π / 180). Factorial is restricted to non-negative integers x ≤ 170.

Example

x = 2, y = 3, Power → 2^3 = 8 (Scientific notation: 8.000000e+0).

Key insights

Logarithmic functions log10(x) and ln(x) are only defined for strictly positive real numbers (x > 0).
Trigonometric functions expect angles in radians for standard mathematical analysis; 180 degrees equals π radians (~3.14159).
Factorials (x!) grow exponentially fast; 70! exceeds 10^100 (a googol) and 171! exceeds double-precision floating-point limits.
Scientific notation (A × 10^k) simplifies working with extremely large or small numbers in physics and chemistry.

How to interpret your result

Primary Result

The exact numerical evaluation of the selected scientific operation.

Scientific Notation

Formats the output as A × 10^k where 1 ≤ |A| < 10, essential for engineering and scientific data.

Exponential Powers

Displays x² and x³ alongside the main calculation for quick polynomial reference.

Frequently asked questions

Why does square root of a negative number show an error?: In real-number mathematics, the square root of a negative number is undefined because no real number squared produces a negative value.
What is the difference between log10 and ln?: log10(x) uses base 10 (common log), whereas ln(x) uses base e ≈ 2.71828 (natural log used in calculus and physics).
How do I convert degrees to radians?: Multiply the angle in degrees by π / 180 (~0.0174533).

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