Scientific Calculator
Type a sum or tap the keys. Trig, logs, powers, roots, factorials and more, with answers as you type, a history tape and fractions.
Exact values are fixed by the SI (2019). G, mₑ, mₚ, ε₀ and μ₀ are CODATA 2022 recommended values.
Press = and your sums appear here. Tap a sum to use it again, or tap an answer to add it to a new sum.
How your answer is worked out
Order of operations: brackets, orders, divide and multiply, then add and subtract.
- 1
Brackets first
(4 − 1) = 3
- 2
Orders: powers, roots, functions
3^2 = 9
- 3
Divide and multiply
3 × 9 = 27
- 4
Add and subtract
2 + 27 = 29Answer: 29
Read more: the order of operations, a worked example, every function and the constants
A scientific calculator follows the same rules as maths teachers do. It doesn't work strictly left to right: it works out brackets first, then powers, roots and functions such as sin or log, then multiplying and dividing, and finally adding and subtracting. This order is called BODMAS in the UK, India and much of the Commonwealth, PEMDAS in the US, and BEDMAS or BIDMAS elsewhere. They are all the same rule.
The formula
Order of operations:
1. Brackets (innermost first)
2. Orders: powers, roots, factorials and functions (powers right to left)
3. Divide and multiply, left to right
4. Add and subtract, left to right
degrees → radians = degrees × π ÷ 180 · gradians → radians = gradians × π ÷ 200
nCr = n! ÷ (r! × (n − r)!) · nPr = n! ÷ (n − r)!
Worked example
Take the starting sum, 2 + 3 × (4 − 1)^2.
- Brackets: 4 − 1 = 3, so the sum becomes 2 + 3 × 3^2.
- Orders: 3^2 = 9, so it becomes 2 + 3 × 9.
- Multiply: 3 × 9 = 27, so it becomes 2 + 27.
- Add: 2 + 27 = 29.
Working strictly left to right would give (2 + 3) × 3^2 = 45, which is wrong. As a fraction 29 is just 29, and in scientific notation it is 2.9 × 10¹.
Rules that catch people out
- −3² = −9. The power is done before the minus sign. Type (−3)² to get 9.
- 2^3^2 = 512. Stacked powers are worked out from the top down: 3² = 9 first, then 2⁹.
- 48 ÷ 2(9 + 3) = 288. A number next to a bracket means multiply, at the same level as ÷, so it goes left to right: 48 ÷ 2 = 24, then 24 × 12. Some textbooks treat 2(9 + 3) as one block and get 2. Add brackets if you mean 48 ÷ (2(9 + 3)).
- 200 + 10% = 220. When you add or take off a percentage, it is a percentage of the number before it, as on phone calculators and Google. On its own, 10% is 0.1, and 200 × 10% = 20.
- sin(30) = 0.5 only in degrees. In radians, sin(30) = −0.988. Check the DEG/RAD switch at the top of the screen.
- −7 mod 3 = 2. The remainder takes the sign of the number you divide by, as in Desmos and most maths software.
Every key
| Key | What it does | Type it as |
|---|---|---|
| sin cos tan | Sine, cosine, tangent in the angle unit chosen | sin(30) |
| sin⁻¹ cos⁻¹ tan⁻¹ | The angle for a sine, cosine or tangent | asin(0.5) |
| sinh cosh tanh | Hyperbolic functions and their inverses | sinh(1), asinh(1) |
| sec csc cot | 1 ÷ cos, 1 ÷ sin, cos ÷ sin | sec(60) |
| ln, log, logₐx | Log base e, base 10, or any base | ln(5), log(100), logb(8, 2) |
| x², x³, xʸ, 10ˣ, eˣ | Powers | 5², 2^10, e^(2) |
| √, ∛, ʸ√x | Square, cube and any root | √(2), ∛(27), root(32, 5) |
| n! | Factorial: 5! = 5 × 4 × 3 × 2 × 1. Non-whole numbers use the gamma function | 5! |
| nCr, nPr | Combinations (order doesn't matter) and permutations (order matters) | nCr(52, 5) |
| mod, gcd, lcm | Remainder, greatest common divisor, least common multiple | 17 mod 5, gcd(12, 18) |
| |x|, ⌊x⌋, ⌈x⌉, round | Absolute value, round down, round up, round to decimals | round(2.675, 2) |
| EE | Times ten to the power, for scientific notation | 6.02ᴇ23 or 6.02E23 |
| Ans | The last answer | Ans × 2 |
| M+ M− MR MC | Add the answer to memory, take it away, recall it, clear it | Saved on this device |
| Rand | A random number from 0 up to 1 | rand() |
Keyboard shortcuts
Type straight into the screen. Enter or = works out the answer, Esc clears, and Backspace deletes. * and / turn into × and ÷. Pressing an operator straight after an answer carries on from it (Ans).
Degrees, radians and gradians
A full turn is 360 degrees, 2π radians or 400 gradians. So 90° = π/2 rad = 100 grad. Schools mostly use degrees; calculus and physics use radians; gradians appear in some surveying work.
Number formats
Advanced mode can show answers rounded to fixed decimal places, in scientific notation (1.2346 × 10⁴) or in engineering notation, where the power of ten is always a multiple of 3 (12.346 × 10³), which matches prefixes such as kilo, mega and micro. The calculator works to about 15–16 significant figures and shows up to 12, so tiny rounding errors such as 0.1 + 0.2 = 0.30000000000000004 are tidied to 0.3.
Constant values: the speed of light, Planck, Boltzmann, Avogadro and elementary charge are exact by the 2019 SI definitions; G, electron and proton mass, ε₀ and μ₀ are CODATA 2022 recommended values. Source: NIST CODATA 2022 tables.
Common questions
What order does a scientific calculator work things out in?
Brackets first, then powers, roots and functions, then multiply and divide from left to right, then add and subtract from left to right. So 2 + 3 × (4 − 1)^2 = 29, not 45, which is what working strictly left to right would give.
Why is −3² equal to −9?
The power is done before the minus sign, so −3² means −(3²) = −9. Type (−3)² to get 9. Stacked powers are also worked out from the top down, so 2^3^2 is 2⁹ = 512. Add brackets whenever you're unsure, and the working stays clear.
Why doesn't sin(30) give 0.5?
The calculator is probably set to radians. sin(30) = 0.5 only in degrees; in radians sin(30) = −0.988. Check the DEG/RAD switch at the top of the screen. A full turn is 360 degrees, 2π radians or 400 gradians. Schools mostly use degrees.
What is 48 ÷ 2(9 + 3)?
This calculator gives 288. A number next to a bracket means multiply, at the same level as divide, so it goes left to right: 48 ÷ 2 = 24, then 24 × 12. Some textbooks treat 2(9 + 3) as one block and get 2, so add brackets if that's what you mean.
How do percentages work on this calculator?
When you add or take off a percentage, it's a percentage of the number before it, as on phone calculators and Google, so 200 + 10% = 220. On its own, 10% is 0.1, so 200 × 10% = 20.
How do I work out combinations and permutations?
Use nCr when order doesn't matter and nPr when it does. nCr = n! ÷ (r! × (n − r)!) and nPr = n! ÷ (n − r)!. For example, type nCr(52, 5) to count the ways of choosing 5 cards from 52.
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