What Online Calculator does
This online calculator works out a full expression in one go instead of one keypress at a time, so you can see and correct everything you entered. Use the on-screen keys or your keyboard for addition, subtraction, multiplication, division, powers, roots, percentages, factorials, logarithms and trigonometry in degrees or radians. Under the answer it lists each step in the order the rules of arithmetic require, and gives the answer as a fraction when one exists. With the starting example, (12 + 8) × 3 − 2^4 ÷ 4, the steps are 12 + 8 = 20, 20 × 3 = 60, 2^4 = 16, 16 ÷ 4 = 4 and 60 − 4 = 56.
What each key types, with an example
Every key adds text to the Calculation box, so anything a key does can also be typed by hand.
| Key | Types | Example | Answer |
|---|---|---|---|
| + − × ÷ | The four basic operators. On a keyboard use + - * / | 100 ÷ 10 × 2 | 20 |
| ( ) | Brackets, worked out before anything outside them | (2 + 3) × 4 | 20 |
| x² and xʸ | ^2 and ^ for powers | 2^10 | 1,024 |
| √ | √( for a square root. sqrt( also works | √(3^2 + 4^2) | 5 |
| % | Percent of the number before it | 250 × 20% | 50 |
| n! | Factorial of a whole number from 0 to 170 | 10! | 3,628,800 |
| sin cos tan | Trigonometry in the chosen angle unit | sin(30) in Deg | 0.5 |
| sin⁻¹ cos⁻¹ tan⁻¹ | asin( acos( atan( for the inverse functions | atan(1) in Deg | 45 |
| ln and log | Natural logarithm and base-10 logarithm | log(1000) | 3 |
| π and e | 3.14159265359 and 2.71828182846 | 4/3 × π × 6^3 | 904.778684234 |
| EE | E, meaning times ten to the power of | 6.02E23 × 2 | 1.204e24 |
| mod | Remainder after division | 17 mod 5 | 2 |
| x⁻¹ | ^(-1), the reciprocal | 5^-2 | 0.04 |
| Ans | The last answer saved with = or Enter | ||
| ⌫ and AC | Delete the last entry, or clear the whole line |
Typed functions that have no key: log2, cbrt, abs, exp, sinh, cosh, tanh, round, floor and ceil.
Worked examples with the steps shown
Each line below is the calculator's own output, including the working.
A shop total
19.99 × 3 + 4.5
64.47. Steps: 19.99 × 3 = 59.97, then 59.97 + 4.5 = 64.47. As a fraction: 6,447/100.
An average of three test scores
(72 + 85 + 90) ÷ 3
82.3333333333, or 82.33 rounded to 2 decimals. Steps: 72 + 85 = 157, 157 + 90 = 247, 247 ÷ 3 = 82.3333333333. As a fraction: 247/3 (82 1/3).
Without the brackets only the 90 would be divided by 3.
Compound growth
1500 × 1.08^5
2,203.9921152, or 2,203.99 rounded. Steps: 1.08^5 = 1.4693280768, then 1,500 × 1.4693280768.
1,500 growing at 8% a year for 5 years. The power is taken before the multiplication.
The long side of a right-angled triangle
√(3^2 + 4^2)
5. Steps: 3^2 = 9, 4^2 = 16, 9 + 16 = 25, √25 = 5.
Choosing 2 items from 5
5!/(3! × 2!)
10. Steps: 5! = 120, 3! = 6, 2! = 2, 6 × 2 = 12, 120 ÷ 12 = 10.
Checking an identity in degrees
sin(30)^2 + cos(30)^2
1. Steps: sin(30°) = 0.5, 0.5^2 = 0.25, cos(30°) = 0.866025403784, squared = 0.75, 0.25 + 0.75 = 1.
The order of operations this calculator follows
A calculation with more than one operator is not read strictly left to right. Brackets come first. Powers and roots come next, and a chain of powers is read from the right, so 2^3^2 is 2^9 = 512. Multiplication, division and mod share the next level and are worked from left to right: 100 ÷ 10 × 2 is 20, not 5. Addition and subtraction come last, also left to right: 10 − 4 + 2 is 8.
Two cases catch people out. A minus sign in front of a power is applied after the power, so -3^2 is -9 while (-3)^2 is 9. And a number written directly against a bracket or a symbol is multiplied, with the same rank as a written × sign: 2π is 2 × π, and 8 ÷ 2(2 + 2) is read as 8 ÷ 2 × 4 = 16. Some textbooks and some handheld calculators give implied multiplication a higher rank and would answer 1, which is why that sum causes arguments. If you mean the other reading, add brackets and the steps table will confirm which one was used.
A simple four-function pocket calculator works differently again: it applies each key as it is pressed, so entering 2 + 3 × 4 on one gives 20. This page gives 14, the answer the standard rules require.
How the percent key works
The % key means two different things depending on what comes before it.
| You type | How it is read | Answer |
|---|---|---|
| 15% | 15 ÷ 100 | 0.15 |
| 250 × 20% | 250 × 0.2, which is 20% of 250 | 50 |
| 45 ÷ 60% | 45 ÷ 0.6, the whole when 45 is 60% of it | 75 |
| 200 + 15% | 200 plus 15% of 200 | 230 |
| 80 − 25% | 80 minus 25% of 80 | 60 |
The + and − behaviour matches the % key on a pocket calculator. For a remainder, use mod, as in 17 mod 5.
Common values worth checking against
| Calculation | Answer | Angle unit |
|---|---|---|
| sin(30) | 0.5 | Degrees |
| sin(45) | 0.707106781187 | Degrees |
| cos(30) | 0.866025403784 | Degrees |
| cos(60) | 0.5 | Degrees |
| tan(45) | 1 | Degrees |
| tan(60) | 1.73205080757 | Degrees |
| sin(1) | 0.841470984808 | Radians |
| atan(1) | 0.785398163397 | Radians |
| √2 | 1.41421356237 | Any |
| ln(10) | 2.30258509299 | Any |
| log(2) | 0.301029995664 | Any |
| 1/3 | 0.333333333333 | Any |
tan(90) in degrees has no value, and the calculator says so instead of returning a huge number.
Precision, rounding and limits
Answers are shown to 12 significant digits. That is enough to hide the tiny binary rounding errors computers make with decimals, so 0.1 + 0.2 shows 0.3 here and 3 × 0.1 shows 0.3. Whole-number answers are shown in full up to 9,007,199,254,740,991. Beyond that, and for anything smaller than 0.000001, the answer switches to E notation: 20! is shown as 2.43290200818e18, meaning 2.43290200818 × 10^18. The largest value it can hold is about 1.8 × 10^308, and the largest factorial is 170!.
The As a fraction line appears when the answer matches a simple fraction to all 12 digits, so 1.375 is also given as 11/8 (1 3/8). For exact fraction arithmetic with full working, the fraction calculator on this site is the better tool.
This is a calculator for real numbers. It does not draw graphs, solve equations for x, store variables or work with complex numbers, so √ of a negative number and the logarithm of zero return a plain-language error. The History holds the last 10 saved lines and is cleared when you leave or reload the page. Nothing you type is sent anywhere.
Step by step
- 1
Tap the number and operator keys, or click the Calculation box and type, for example 19.99 × 3 + 4.5. The first number key you press replaces the example.
- 2
Read the answer on the display line under the box. It changes with every key, so there is no need to press = first.
- 3
For sin, cos and tan, set the Angle unit switch to Deg or Rad before reading the answer.
- 4
Press = or Enter to save the line to the History and carry the answer into the next calculation. The Ans key types the last saved answer.
- 5
Check the Order of operations, step by step table to see how the answer was reached, then use Copy the calculation to take the whole line with you.