Calculator & Scientific Calculator

About Calculator & Scientific Calculator

There are two calculators on this page. Basic mode works like a phone or desk calculator and evaluates in the order you press keys. Scientific mode reads a whole expression at once and follows operator precedence. Enter 2 + 3 × 4 and basic mode shows 20 while scientific mode shows 14. Neither is broken; they follow different rules, and not knowing which rule you are using is how people end up trusting a wrong answer.

What follows covers where the two approaches diverge and the cases that make calculators look strange: 0.1 + 0.2, the percent key, degrees versus radians, and the infamous 6÷2(1+2). Each is explained in terms of what this tool actually does, not what calculators do in general.

Calculators that follow key order vs. ones that read formulas

Basic mode uses immediate execution. Each time you press an operator, the result so far is locked in. In 2 + 3 × 4, pressing × turns 2 + 3 into 5, and then 5 is multiplied by 4 to give 20. That behavior suits running totals, like adding up receipts or continuing from the last answer. Most cheap pocket calculators, and the portrait layout of many phone calculators, have historically worked this way.

Scientific mode parses the entire line before evaluating it. Multiplication and division come before addition and subtraction, and powers come before both. In this tool -3^2 is -9 (the power is applied first, then the sign) and 2^3^2 is 2^9 = 512 (powers group from the right). Excel's =-3^2 returns 9, so if you are checking a spreadsheet, add parentheses to make the intent explicit.

Most viral posts about calculators "disagreeing" come down to this difference. If an expression mixes multiplication with addition, type it into scientific mode as a single line instead of keying it step by step.

Why 0.1 + 0.2 shows 0.3 here

Computers store numbers in binary floating point (IEEE 754 double precision). 0.1 has no finite binary representation, so it is stored as the nearest approximation, and in raw JavaScript 0.1 + 0.2 evaluates to 0.30000000000000004. In both modes this tool computes at full precision and hides that noise only when displaying the result; the two modes just round the display to a different number of digits.

Basic mode shows results rounded to 10 decimal places, so 0.1 + 0.2 displays as 0.3. The rounding applies to the screen only; the next operation receives the full-precision value. 1 ÷ 3 = displays 0.3333333333, yet pressing × 3 = next gives 1, not 0.9999999999. A calculator that rounded the stored value at every step would show 0.9999999999 here.

Scientific mode keeps full precision while computing and only rounds to 12 significant digits for display. 1/3*3 returns 1 and 0.1*3 returns 0.3. To avoid accumulated error, write the whole calculation as one expression or reuse Ans instead of retyping a rounded intermediate value.

The percent key follows the same rule in both modes

Basic mode follows the convention of ordinary desk calculators. With + or − pending, % converts the current number into that percentage of the first number: 200 + 10 % = gives 200 + 20 = 220, and 200 − 10 % = gives 180. With × or ÷ pending, or no operation at all, it just divides by 100, so 200 × 10 % = gives 20. This makes sales-tax and discount calculations quick: 49.99 + 8.25 % = adds 8.25% tax.

Scientific mode uses the same rule. When the term right after + or − is b%, a + b% = a × (1 + b/100) and a − b% = a × (1 − b/100), so 200+10% is 220 and 200-10% is 180. Everywhere else % divides by 100: 200*10% is 20 and 50% is 0.5. The rule only applies when the % term is the whole right-hand operand, so 200+10%*2 is 200 + 0.2 = 200.2. When a number, bracket or name follows % directly, it is read as the remainder: 7%3 is 1, the same as mod(7,3).

Degrees vs. radians

Scientific mode starts in DEG, so sin(30) is the sine of 30 degrees, exactly 0.5. Switch the angle button to RAD and the same input means 30 radians, giving about -0.988. Physics formulas and programming languages almost always assume radians, so if a textbook answer does not match, check the mode first. A third option, GRAD, divides a full turn into 400 units and is rarely needed outside surveying.

You can also mark units inline without changing the mode: in RAD mode, sin(30°) returns 0.5 because the ° symbol converts just that number. Results at special angles are cleaned up, so cos(90°) is 0 and sin(pi) in RAD mode is 0 rather than the 1.2×10^-16 that raw floating point produces. Inside derivatives, integrals and solve(), the tool always uses radians regardless of the mode.

Is 6÷2(1+2) equal to 1 or 9?

When the multiplication sign before a parenthesis is left out, readers disagree. Treat multiplication and division as equal and go left to right and you get 6÷2×3 = 9. Treat the implied multiplication as binding more tightly and you get 6÷(2×3) = 1. There is no single international rule that settles it, and calculator makers do not agree either: different models of the same brand have given different answers.

This tool's scientific mode binds implied multiplication, as in 2(1+2), 2pi or 3sin(x), more tightly than an explicit × or ÷. So 6÷2(1+2) gives 1, and with x = 4, 1/2x gives 1/(2×4) = 0.125. If you meant half of x, write (1/2)x or 1/2*x. Writing every operator explicitly is the only way to get the same answer on every calculator.

Worked examples

How to use it

1. Choose Basic or Scientific with the tabs at the top.
2. In basic mode, press numbers and operators in sequence and finish with =.
3. In scientific mode, type the whole expression and press =. Check the DEG/RAD indicator before using trig functions.

Frequently asked questions