Scientific Calculator

About the Scientific Calculator

A scientific calculator earns its place the moment a problem involves an angle, a logarithm, a power, or a factorial. This one gives you a single expression line and a keypad. You type or tap a whole formula, such as 1500*(1+0.05)^10, and the answer appears underneath and updates with every keystroke. Parentheses and the standard order of operations are respected, so you can write a formula the way a textbook prints it rather than working through it one button at a time.

Behind the display sits the mathjs expression engine, a widely used JavaScript math library, with one customization: a DEG/RAD switch. Trigonometric functions need to know whether 30 means thirty degrees or thirty radians, and the switch decides. In DEG mode (the default), sin(30) is 0.5. In RAD mode, the same input is the sine of thirty radians. Results are rounded to 12 significant digits, which hides the tiny floating-point residue that makes a plain 0.1 + 0.2 appear as 0.30000000000000004 in many tools.

Students, engineers, tradespeople, and anyone checking compound growth or physics formulas can use it. Because you can type, the engine also accepts functions that have no button, such as asin, acos, atan, exp, abs, and cbrt, and two-argument forms such as log(8, 2). The sections below explain the quirks that matter most in practice, particularly what the ln and log buttons really insert and how rounding behaves for very large and very small answers.

When to Use It

How to Use It, Step by Step

1. Choose the angle mode first with the DEG and RAD buttons at the top left. DEG is selected when the page opens. Pick RAD only if your formula supplies angles in radians, such as pi/6.
2. Click the expression line, which shows 0 when empty, and start typing a formula using your keyboard, or tap buttons in the keypad. Both can be mixed freely in the same expression.
3. Use the keypad's function buttons to insert text. sin, cos, and tan add an opening parenthesis, so finish with the matching closing parenthesis. The root button inserts sqrt( and the power button xʸ inserts a caret.
4. Know what the log buttons insert. The button labeled ln inserts log(, which is the natural logarithm, and the button labeled log inserts log10(, the base-10 logarithm. Typing ln( by hand is not recognized.
5. Add constants with the π and e buttons, which insert pi and e, or type pi and e. Use the exclamation-mark button for factorial, as in 5!, and the parentheses buttons to group terms.
6. Read the live answer shown beneath the expression, starting with an equals sign. While a bracket is still open you may see "Error", which simply means the expression is incomplete. "Undefined" means the math has no finite value, such as 1/0.
7. Press the "=" button or the Enter key to move the result into the expression line so you can keep calculating with it. Use C to clear everything or the backspace button to remove the last character, and Copy to copy the result.

Understanding Your Results

The displayed result is rounded to 12 significant digits, and trailing zeros are dropped, so 9.99*3 appears as 29.97 and 100*1.1 as 110. Very small or large results switch to scientific notation: 1.22464679915e-16 means 0.000000000000000122..., and 7.25741561531e+306 is the value of 170 factorial. The rounding is good for most purposes, but it does mean that a product with more than twelve meaningful digits is shortened; 123456789*987654321 shows 121932631113000000, not the exact 121932631112635269.

Trigonometric answers can show a tiny leftover instead of an exact zero. In DEG mode, sin(180) displays 1.22464679915e-16 and cos(90) displays 6.12323399574e-17, because the angle is first converted to radians using an approximate value of pi. Treat any value around e-16 or e-17 as zero. Likewise tan(90) does not report Undefined; it returns 16331239353200000, an enormous number that signals the tangent is undefined for practical purposes.

Some results are not ordinary numbers. The square root of a negative number returns a complex value written as text, so sqrt(-4) displays 2i. An arcsine of a value above 1 is Undefined in DEG mode but is shown as a complex number in RAD mode. If an answer includes the letter i, the expression went outside the real numbers. Check for a sign error, a missing parenthesis, or a value outside a function's domain.

More Worked Examples

Tips for Better Results

• Use the ln button for natural logarithms and the log button for base-10. If you type by hand, remember that log( is natural, log10( is base 10, and log(x, b) uses base b, so log(8, 2) returns 3.
• Set DEG or RAD before you type the formula. Formulas with pi, such as sin(pi/6), are written in radians, so switch to RAD for them; in DEG mode, sin(pi/6) would treat the input as about 0.52 degrees.
• Only sin, cos, tan, asin, acos, and atan follow the DEG setting. Other trig-style functions such as sec, cot, and sinh always use radians, so convert angles by hand for those.
• Check order of operations when a result looks off. Exponents bind tighter than a leading minus, so -2^2 is -4, and stacked powers run right to left, so 2^3^2 is 2^9 = 512. Add parentheses to make your intent explicit.
• Add parentheses around every denominator and exponent that has more than one term, such as 1/(2+3) or 2^(1/3). A missing pair is the most common cause of a wrong answer.
• Percent signs follow the engine's rules, not a pocket calculator's: 200*20% returns 40 and 20% returns 0.2, while a % between two numbers means remainder, so 10 % 3 returns 1.

Common Mistakes to Avoid

• Typing ln(10) and expecting a natural log. The word ln is not recognized and gives Error. Use the ln button, or type log(10) for the natural logarithm.
• Assuming log(100) gives 2. In this calculator, log( is the natural logarithm; for base 10 use the log button or type log10(100).
• Leaving the mode on DEG while entering radian formulas, or the reverse. A sine of 1 in the wrong mode gives 0.0174524064373 instead of 0.841470984808.
• Typing a unit such as 30 deg inside a trig function in DEG mode. The mode already treats numbers as degrees, and the extra unit makes the result Undefined.
• Reading an unmatched bracket as a wrong answer. The display shows Error until every opening parenthesis has a closing one, so finish the expression before judging the result.

Assumptions and Limits

• Calculations use standard double-precision floating-point numbers, with results trimmed to 12 significant digits. Expect rounding differences in the last digit compared with a handheld calculator that carries different internal precision.
• Very large integer results lose exactness after about 12 digits in the display, and numbers beyond roughly 1.8 x 10^308 overflow to Undefined.
• Only six trig functions are switched by the DEG/RAD setting. Hyperbolic, secant, cosecant, and cotangent functions treat their input as radians in either mode.
• This calculator is a convenience for homework, estimates, and quick checks. For engineering design, medical dosing, structural, or financial decisions, verify the result with a second method and follow the standards of your field.

Key Terms

Order of operations

The rule for deciding which part of a formula is calculated first: parentheses, then exponents, then multiplication and division, then addition and subtraction.

Radian

An angle unit based on the circle's radius. A full turn is 2 pi radians, or 360 degrees, so 180 degrees equals pi radians.

Natural logarithm

The logarithm to base e, about 2.71828. It answers the question: e raised to what power gives this number? This calculator's log( function is the natural logarithm.

Factorial

The product of all whole numbers from 1 up to a given number, written with an exclamation mark. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

Significant digits

The digits in a number that carry meaning, counted from the first non-zero digit. This tool shows up to 12 of them.

Complex number

A number with a real part and an imaginary part written with i, where i squared equals -1. The square root of -4 is the complex number 2i.