Scientific Calculator: Roots, Powers, Logs & Trig Functions

Q: Are trigonometric angles in degrees or radians?

Angles are entered in **degrees**. The calculator converts degrees to radians before evaluating sine, cosine, or tangent: $$ \text{Radians} = \text{Degrees} \times \frac{\pi}{180} $$ For example, $30^\circ \times \pi / 180 = \pi/6$, so $\sin(30^\circ) = 0.5$.

Q: What is the difference between log and ln?

**log** means base-10 logarithm in this calculator, while **ln** means natural logarithm with base $e \approx 2.71828$. Examples: $\log_{10}(1,000) = 3$ because $10^3 = 1,000$, and $\ln(e) = 1$ because $e^1 = e$.

Q: Why does the calculator show undefined for some inputs?

The real-number operations have domain limits. Examples: - $\sqrt{-4}$ is not a real number. - $\log_{10}(0)$ is undefined. - $\ln(-5)$ is undefined in real numbers. - $\tan(90^\circ)$ is undefined because $\cos(90^\circ) = 0$. Use a complex-number calculator if you need non-real roots or logarithms.

Q: How many decimals should I keep?

Keep enough digits for the next step, then round only at the end. For a classroom problem, follow the teacher or textbook rule. For measurements, match the precision of the inputs: if the angle is measured to the nearest **1 degree**, reporting ten decimal places usually implies more precision than the measurement supports.

Result

√a

Input (a)

Operation

√a

Input (a)9

Result3

√a = 3

How this calculator works

Use the explanation to understand the formula, assumptions, and practical limits behind the calculator result.

What This Scientific Calculator Handles

This calculator evaluates one input at a time using common scientific operations: square root, square, cube, base-10 logarithm, natural logarithm, sine, cosine, tangent, and absolute value. It is useful for quick checks in algebra, geometry, trigonometry, science classes, spreadsheets, and engineering estimates.

Operation Rules

Operation	Formula or meaning	Important rule
Square root	$\sqrt{a}$	Real result only when $a \ge 0$
Square	$a^2$	Works for positive and negative values
Cube	$a^3$	Keeps the sign of $a$
Log base 10	$\log_{10}(a)$	Real result only when $a > 0$
Natural log	$\ln(a)$	Real result only when $a > 0$
Sine / cosine / tangent	$\sin(a^\circ)$ , $\cos(a^\circ)$ , $\tan(a^\circ)$	Input angle is in degrees
Absolute value	$	a

For trigonometry, the calculator accepts degrees and converts internally to radians:

\text{Radians} = \text{Degrees} \times \frac{\pi}{180}

Worked Examples

$\sqrt{81} = 9$
$\log_{10}(1,000) = 3$
$\ln(e) = 1$
$\sin(30^\circ) = 0.5$
$|-12| = 12$

When a Result Is Undefined

Some operations have domain limits. $\sqrt{-9}$ is not a real number, and $\log_{10}(0)$ or $\ln(-5)$ is undefined in real-number arithmetic. Tangent is also undefined when cosine is zero, such as at $90^\circ$ plus full $180^\circ$ rotations.

How to Read the Result

Use the result as a numeric check, then keep enough decimal places for the next step. If the answer feeds into a larger calculation, avoid rounding too early. For official exams, technical reports, or engineering work, follow the required rounding and significant-figure rules.

Frequently asked questions

Are trigonometric angles in degrees or radians?

What is the difference between log and ln?

Why does the calculator show undefined for some inputs?

How many decimals should I keep?