Scientific Calculator

A full scientific calculator — trig, logs, powers, factorials and fractions — with live results, history and keyboard input.

Expression

Result

History

Press = or Enter to keep a result here. The list stays on this device.

Type an expression or press the keys, and the result appears as you go: 2 sin(60) + √8 in Deg gives 4.56047793232. Fractions, multiples of π and square roots can be kept exact, so 1/3 + 1/6 is 1/2 and sin(60) is √3/2. Results you keep go into a history you can reuse.

How to use it

Expression takes typing, pasting and the on-screen keys alike, up to 1,000 characters. A function key writes its name and an open bracket, which you close with ). Numbers are typed without digit grouping, because a comma separates the values of a function.
Deg / Rad / Grad sets the angle unit that sin, cos and tan read and that their inverses give back. It opens on Deg.
Decimal / Exact chooses the form of the large result. Where a result has an exact form, the other form is shown beside it; where it has none, Exact shows the decimal and says so.
= or Enter keeps the result in History, which holds the last 100 on this device. Click an expression there to work on it again, or its result to write it into the current expression. Ans is the last result kept. After =, an operator carries on from Ans and a number starts a new expression.
2nd turns sin, cos, tan and their hyperbolic keys into the inverses, ln into eˣ and log into 10ˣ.
M+ and M− add the current result to memory or subtract it, MR writes the memory into the expression and MC clears it. Memory lasts until the page is closed or reloaded.

On a keyboard, beyond typing the expression itself:

Enter or = — keeps the result in the history.
Esc — clears the expression.
↑ and ↓ — bring back earlier expressions.
Ctrl + Z, Ctrl + Y — undo and redo.
* / - — written as × ÷ −.

Decimal results are shown to 12 significant figures, in scientific notation from 10¹² and below 10⁻⁶: 2^70 is 1.18059162072 × 10²¹. Everything runs in your browser.

How an expression is read

From first to last: brackets; the postfix signs ! and %; powers, from right to left; a leading minus; multiplication, division and mod, from left to right; then addition and subtraction. Two values written side by side are multiplied, at the same level as × and ÷. Calculators and textbooks do not all agree on that last rule, so where the grouping could be doubted, Read as above the result writes it out:

6÷2(1+2) is read as (6 ÷ 2) × (1 + 2) and gives 9.
1/2π is read as (1 ÷ 2) × π and gives 1.57079632679. For 1 over 2π, write 1/(2π), which gives 0.159154943092.
-3^2 is read as −(3^2) and gives −9, while (-3)^2 gives 9.
2^3^2 is read as 2^(3^2) and gives 512.

A function typed without brackets takes the term that follows: one value with its powers and the values written against it, up to the next operator or function name. So sin 30^2 is read as sin(30^2) and gives 0, and sin30cos30 is sin(30) × cos(30). √ and ∛ take one value only: √2π is read as √(2) × π and gives 4.44288293816.

A percent sign divides by 100 wherever it stands, so 50 + 10% is 50.1. Phone calculators read that as 50 plus 10% of 50; a note under the result says how to enter that instead.

Exact results cover fractions, a fraction times π, and a fraction times a square root. Products and quotients stay exact where the result has one of those forms, and sums only of like terms: √2 × √6 is 2√3 and 2π + π/2 is 5π/2, but 1 + √2 is shown as 2.41421356237 only. At multiples of 30° and 45°, in any angle unit, sin, cos and tan use the exact value, so sin(π) in Rad is 0 and not the 1.22464679915 × 10⁻¹⁶ that floating-point arithmetic gives, and tan(90) in Deg is refused (“tan is undefined here”).

A factorial of a whole number is exact up to 170!, the largest a decimal result can hold; of any other number it is the gamma function, Γ(n + 1), so 0.5! is 0.886226925453. A negative number has a real root only for an odd root: (-8)^(1/3) is −2, while (-8)^0.5 shows “No real result”.

Examples

6 ÷ 2(1 + 2)

Typed as 6÷2(1+2), this is read as (6 ÷ 2) × (1 + 2): the division comes first because it stands first, and the result is 9. For 6 over 2(1 + 2), type 6÷(2(1+2)), which gives 1.

The sine of 30, in degrees and in radians

With Deg chosen, sin(30) is 0.5. With Rad, the same expression is −0.988031624093, the sine of 30 radians. An unexpected trig result is most often the wrong angle unit.

A logarithm to base 2

log_2(1024) is 10, because 2 to the power 10 is 1,024. The key log_b writes log_; type the base, then the value in brackets. log(x) alone is base 10 and ln(x) is base e.

Ways to choose 5 cards from 52

52C5, or nCr(52, 5), is 2,598,960. Where the order of the cards matters, 52P5 is 311,875,200, which is 120 times as many: 5! is the number of orders of five cards.

An exact answer

In Deg, 2 sin(60) is 1.73205080757 as a decimal. Choose Exact and the result reads √3, with the decimal beside it.

What you can type

Typed forms, their keys and an example of each

Typed	Key	Meaning	Example
`2E3`	EXP	× 10 to a power	`2.5E3` = 2,500
`pi or π, e`	π, e	The constants	`2π` = 6.28318530718
`sqrt(x) or √x`	√	Square root	`√16` = 4
`cbrt(x) or ∛x`	³√	Cube root	`∛27` = 3
`nthroot(n, x)`	ⁿ√	nth root	`nthroot(4, 81)` = 3
`x^y`	xʸ	Power	`2^10` = 1,024
`log(x), ln(x)`	log, ln	Log to base 10 and base e	`log(1000)` = 3
`log_b(x)`	log_b	Log to base b	`log_3(81)` = 4
`n!`	n!	Factorial	`5!` = 120
`nPr(n, r) or n P r`	nPr	Permutations	`5P2` = 20
`nCr(n, r) or n C r`	nCr	Combinations	`5C2` = 10
`a mod b`	mod	Remainder, with the sign of b	`-7 mod 3` = 2
`abs(x) or \|x\|`	\|x\|	Absolute value	`\|3 − 5\|` = 2
`x%`	%	x ÷ 100	`10%` = 0.1
`asin(x) or arcsin(x)`	2nd, sin	Inverse sine	`asin(0.5)` = 30
`sinh(x)`	sinh	Hyperbolic sine	`sinh(1)` = 1.17520119364

Frequently asked questions

Many programs show 0.30000000000000004, because binary floating point cannot hold 0.1 or 0.2 exactly. This calculator works typed decimals out as exact fractions wherever it can, so the sum is 3/10, shown as 0.3.

Degrees divide a full turn into 360, radians into 2π and gradians into 400. School geometry and everyday angles use degrees; calculus and physics formulas use radians; gradians appear in surveying. A right angle is 90°, π/2 rad or 100 grad, and asin(1) gives 90, π/2 or 100 in the three units.

Multiply by 1 plus the percentage: 50 plus 10% is 50 × 1.1, which gives 55. Typed as 50 + 10%, the result is 50.1, because 10% is the number 0.1. The Percentage Calculator handles increases, decreases and changes directly.

Its exact value, (√6 − √2)/4, is a sum of two different roots, and the exact forms here are a single fraction, multiple of π or multiple of one square root. The decimal, 0.258819045103, is shown alone.