DeluxeCalc

Scientific Calculator

Evaluate expressions with trigonometry, logarithms, powers, roots, and factorials.

About this calculator

A scientific calculator goes beyond basic arithmetic. It handles powers, roots, logarithms, factorials, and trigonometric functions, and it follows the standard order of operations so that 2 + 3 × 4 gives 14, not 20. This online scientific calculator evaluates a whole expression at once, so you can type a formula the way it appears in your textbook and see the answer immediately.

How to use this calculator

Type an expression into the box or build it with the keypad. Function keys such as sin, ln, and √ insert the function name with an opening bracket, so you type the argument and then close the bracket yourself. The result updates as you type. If the expression cannot be worked out, a short message appears in place of the result, such as Missing closing bracket or Result is undefined. Press = or Enter to replace the expression with its result so you can keep calculating from there. The C key clears the expression and the backspace key removes the last character. Every expression and the chosen angle mode are saved in the page address, so you can bookmark or share a calculation exactly as you entered it. Expressions can be up to 500 characters long.

Supported functions

Sin, cos, and tan for trigonometry; asin, acos, and atan for the inverse functions (shown as sin⁻¹, cos⁻¹, and tan⁻¹ on the keypad); sinh, cosh, and tanh for the hyperbolic functions; ln for the natural logarithm and log for the base-10 logarithm; sqrt or √ for the square root and cbrt for the cube root; abs for absolute value; and exp for e raised to a power. The operators are + and −, × or * for multiplication, ÷ or / for division, ^ for powers (the x² key inserts ^2), ! for factorial, and % for percent. The constants pi (or π) and e are built in. Function names are not case-sensitive, so SIN(30) works too, and numbers can be written in scientific notation, so 2e3 means 2000.

Order of operations

Brackets are worked out first, then powers, then multiplication and division from left to right, then addition and subtraction. Powers are evaluated from right to left, so 2^3^2 means 2^9, which is 512. A minus sign in front of a power applies after the power, so −2^2 is −4, while (−2)^2 is 4. A negative exponent needs no brackets, so 2^-1 gives 0.5. Factorial (!) and percent (%) apply to the number directly before them, so 5! is 120 and 200 × 15% is 30.

Implied multiplication

You can leave out the multiplication sign, just as you would on paper, so 2π, 3(4 + 1), and 5 sin(30) all work. Implied multiplication has the same priority as an ordinary multiplication sign and is worked out from left to right. That means 1/2π is read as (1/2) × π, which is about 1.57079632679, not 1/(2π), which is about 0.159154943092. When in doubt, add brackets.

Degrees and radians

The trigonometric functions sin, cos, and tan read their input in the selected angle mode, and the inverse functions asin, acos, and atan return their answer in that mode. In degrees, sin(30) is 0.5 and atan(1) is 45. In radians, sin(π/2) is 1 and cos(π) is −1. The hyperbolic functions do not use angles, so the mode does not affect them.

Worked example

A 6 metre ladder leans against a wall at 75° to the ground. How high up the wall does it reach? The height is the side opposite the angle, so height = 6 × sin(75°). With the calculator in degree mode, type 6 sin(75) and the result is 5.79555495773, so the ladder reaches about 5.80 metres. To find the hypotenuse of a right triangle with sides 3 and 4, type √(3^2 + 4^2) and the result is exactly 5. To count the ways of choosing 2 items from 4, type 4!/(2! × 2!) and the result is 6.

Precision and how results are shown

Results are rounded to 12 significant digits. This hides the tiny errors that computers make with decimal fractions, so 0.1 + 0.2 shows 0.3 rather than 0.30000000000000004, and sin(30) shows 0.5 even though the raw value is a hair below it. Results from the trigonometric functions that are within 10⁻¹⁵ of zero are shown as 0, so sin(180) and cos(90) in degrees both give 0. Very large or very small answers use e notation; for example, 170! shows as 7.25741561531e+306.

When a result is undefined

The calculator reports Result is undefined for division by zero, the square root of a negative number, the logarithm of zero or a negative number, asin or acos of a value outside −1 to 1, tan of 90°, 270°, and other odd multiples of 90° (or of π/2 in radian mode), and factorials larger than 170!. A factorial of a number that is not a whole number, such as 1.5!, gives the message Factorial needs a whole number ≥ 0. Writing sin30 without brackets gives an error because every function needs its argument in brackets.

Common mistakes and limitations

The percent key always means divide by 100, so 200 + 10% gives 200.1, not 220. To add 10% to 200, type 200 + 200 × 10% or 200 × 1.1, both of which give 220. Check the angle mode before any trigonometry; sin(30) in radian mode is about −0.988, which is the most common source of wrong answers. Remember that log is base 10 and ln is base e. A negative number raised to a fractional power, such as (−8)^(1/3), is reported as undefined, so use cbrt(−8), which gives −2. For other roots, use a fractional power such as 16^(1/4), which gives 2. This calculator works with real numbers only: it has no complex numbers, variables, memory keys, or calculation history.

Frequently Asked Questions

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