Order of operations (BODMAS / PEMDAS)
When an expression has several operations, the calculator works them out in a fixed order, the same one taught in schools. BODMAS (Brackets, Orders, Division/Multiplication, Addition/Subtraction) and PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) are two names for the same rule.
- Brackets first, innermost outwards.
- Functions and postfix operators: sin, √, log, n!, x², %.
- Powers (xʸ), worked right to left: 2^3^2 = 2^9.
- Unary minus: −2² means −(2²).
- Multiplication and division, left to right.
- Addition and subtraction, left to right.
| Expression | Worked as | Result |
|---|---|---|
2+3×4 | 3×4 first, then +2 | 14 |
(2+3)×4 | brackets first: 5×4 | 20 |
2^3^2 | right to left: 2^9 | 512 |
−2^2 | −(2²) | −4 |
(−2)^2 | (−2)×(−2) | 4 |
3!^2 | 6² | 36 |
6÷2(1+2) | 6÷2×3, left to right | 9 |
You can leave out the × sign before a bracket, a constant or a function: 3(4+5) = 27, 2π = 6.28318530718 and 2sin(30) = 1 in degree mode. Implied multiplication has the same priority as an ordinary ×, so 6÷2(1+2) is 9. If you mean 6 ÷ 6, write 6÷(2(1+2)). A missing closing bracket at the end is added for you.
Degrees vs radians
Trigonometric functions need to know the unit of the angle. A full turn is 360 degrees or 2π radians, so 180° = π rad and 1 rad ≈ 57.2958°.
Use DEG for everyday geometry, surveying and navigation, and RAD for calculus, physics and most programming languages. The same keys give very different answers: sin(30) is 0.5 in DEG mode but −0.988031624093 in RAD mode, because 30 radians is almost five full turns. In DEG mode, inverse functions also return degrees, so sin⁻¹(0.5) = 30.
Functions on this calculator
| Key | Meaning | Example |
|---|---|---|
| x², xʸ | square, any power | 2^10 = 1024 |
| √, ∛ | square root, cube root | √16 = 4, ∛(−8) = −2 |
| 1/x | reciprocal (shown as ⁻¹) | 4⁻¹ = 0.25 |
| ln, log | natural log (base e), common log (base 10) | ln(e) = 1, log(1000) = 3 |
| n! | factorial of a whole number | 5! = 120 |
| % | divides by 100; after + or − it takes that percentage of the number before it | 200×10% = 20, 50+10% = 55 |
| EXP | × 10 to the power | 6.02E23 = 6.02 × 10²³ |
| Ans, MR | last answer, memory | Ans+1 |
Accuracy and error messages
Results are shown to 12 significant digits, which hides the tiny binary rounding errors every computer makes: 0.1+0.2 shows 0.3, not 0.30000000000000004. Very large or very small numbers switch to E notation, such as 2.43290200818E18 for 20!. Instead of a vague "Error", the calculator tells you what went wrong: dividing by zero, the square root or logarithm of a negative number, ln(0), sin⁻¹ of a value outside −1 to 1, tan(90°), or the factorial of a non-whole number.
For everyday percentages, the percentage calculator is quicker, and the unit converter handles lengths, weights and temperatures.
Frequently asked questions
Does this calculator follow BODMAS / PEMDAS?
Why is −2² equal to −4?
How do I switch between degrees and radians?
How do I enter a number like 6.02 × 10²³?
What do MC, MR, M+ and M− do?
Why does 0.1 + 0.2 show 0.3 here but not in some apps?
Last updated . How we check our tools.