Scientific & Standard Calculator

A calculator that reads the whole expression, not one keystroke at a time

Most on-screen calculators work like the cheap pocket models they imitate: you press a number, then an operator, then another number, and each press immediately changes a running total. That design cannot respect the order of operations, because it has already thrown away the earlier part of the sum by the time you reach the end. Type 2 + 3 × 4 on one of those and you get 20, because it adds 2 and 3 first and then multiplies by 4. The mathematically correct answer is 14: multiplication binds tighter than addition, so the 3 × 4 happens first.

This tool keeps the entire expression as text and evaluates it only when you press equals. Behind the display is a small recursive-descent parser — the same technique programming languages use to read source code. It walks the string once, honouring precedence (parentheses, then functions and powers, then × ÷ %, then + −), and produces a single answer. That is why 2 + 3 × 4 returns 14 here, and why (2 + 3) × 4 returns 20: the brackets force the addition to happen first.

Why there is no eval() here, and why that matters

The lazy way to build a browser calculator is to hand the typed string to JavaScript's eval() function and let the language do the arithmetic. It works, but it is a genuine security and correctness hazard: eval executes any JavaScript, not just maths, so a crafted input could run code, and it silently accepts nonsense that a calculator should reject. It also has no concept of degree versus radian, factorials, or the ∛ symbol — those are not part of the language.

The parser in this tool only understands numbers, the constants π and e, the operators and functions on the keypad, and parentheses. Anything else is reported as a Math Error instead of being executed. Because it is a closed grammar, it can also add conveniences a raw language evaluator cannot: it treats a number written directly before a bracket or constant as multiplication, so 2(3+4), 2π, and 2sin(30) all behave the way they read on paper.

Degrees versus radians: the setting that quietly changes every answer

The single most common mistake with any scientific calculator is computing a trig function in the wrong angle unit. A degree is one 360th of a full turn — the unit you met first in geometry. A radian measures the same angle by the length of arc it cuts on a unit circle, so a full turn is 2π radians, roughly 6.283. They describe the same angles in different numbers: 180° and π radians are identical, and 30° is π/6.

The gap is not subtle. In Degree mode sin(30)is exactly 0.5, because 30° is a familiar angle. Switch to Radian mode and the same keystrokes give about −0.988, because now the calculator reads "30 radians" — nearly five full turns around the circle. Neither answer is wrong; they answer different questions. School trigonometry and most engineering coursework work in degrees, while calculus and physics usually work in radians, because the neat derivative and series results for sine and cosine only hold when the angle is in radians. Set the DEG/RAD switch to match the problem in front of you before you press a trig key, and check the little label if an answer looks surprising.

What the function keys actually compute

log and ln are two different logarithms. logis base 10, the answer to "ten to what power gives this number" — log(1000) is 3. ln is the natural logarithm, base e (about 2.718), which appears throughout growth, decay, and compound-interest maths. Both are undefined for zero and negative inputs, so the tool returns a Math Error rather than a fake number.

The roots and powers. √ is the square root and rejects negatives, since no real number squares to a negative. ∛ is the cube root and happily accepts negatives, because a negative number does have a real cube root (∛−8 = −2). xʸ raises the first value to the power of the second and is right-associative, so 2^3^2 is 2^(3^2) = 512, not (2^3)^2 = 64 — the standard mathematical convention.

The factorial (x!) multiplies every whole number from 1 up to the input: 5! = 5 × 4 × 3 × 2 × 1 = 120. It is only defined for non-negative whole numbers, so a decimal or negative input returns a Math Error. Factorials grow explosively — 170! is already near the largest number JavaScript can hold — so beyond that the tool reports infinity rather than a meaningless figure.

Memory keys, history, and keyboard use

The memory register is a single stored number that survives across calculations. Press MS to store the current display, MR to bring it back, and M+ or M- to accumulate a running total without writing intermediate results on paper — useful when you are summing a column of products, for example. MC clears it. A badge shows the stored value whenever it is not zero.

Every evaluation is also added to the session history on the side. Click any entry to reload its result to the display and carry on calculating from it. The history lives only in the page: refresh or close the tab and it is gone, which is deliberate — nothing about your calculations is stored or sent anywhere. If you prefer the keyboard, the digits, the four basic operators, parentheses, the exponent caret, and the factorial mark are all mapped, with Enter for equals, Backspace to delete a character, and Escape or C to clear.