Calculate a Basic Expression and Keep Its Trace

Reviewed concrete example

A strict expression lane with visible state

This online calculator with tape is the site’s full arithmetic scratchpad. Type with a keyboard or press the same labeled controls. The page shows what was normalized, what result was produced, which operations were resolved first, and where an invalid expression stopped.

There is no server-side calculator. The complete route—from character tokenization through rational arithmetic and the running tape—operates in the browser. The calculator does not pass input to eval, construct a function, call a remote endpoint, write local storage, or hide a correction.

Understand the accepted grammar

Numbers use ASCII digits and at most one decimal point. A leading decimal such as .5 normalizes to 0.5; a trailing decimal point is rejected until another digit is supplied. Addition and subtraction have lower precedence than multiplication and division. Parentheses create explicit groups. A minus sign can be unary at the beginning of an expression or after another operator or opening parenthesis.

Percent is postfix. It divides the value immediately to its left by 100, including a completed parenthesized group. (-25)% is -0.25. Only one postfix percent is allowed for a primary value. A second consecutive % is rejected at its source position whether it was typed or pressed on the keypad, so 10%% never receives a silent interpretation.

There is no implicit multiplication. 2(5) and (2)(5) report an operator error. Exponent notation, commas, letters, units, currency signs, square roots, and functions are outside scope.

Worked expression: unary signs, grouping, and percent

Enter -(12.5 - 2.5) × (1 + 5%). Tokenization identifies unary minus, an opening group, two decimals, subtraction, multiplication, a second group, addition, and postfix percent. The first group becomes 10. The postfix value 5% becomes 0.05, so the second group becomes 1.05. Unary minus makes the first group -10. Multiplication produces -10.5.

The normalized expression reads −(12.5 − 2.5) × (1 + 5%). The order summary lists inner subtraction, postfix percent, inner addition, unary negation, and final multiplication. A result card shows -10.5 and can show -21/2 as the exact rational form.

Pressing Enter adds exactly one tape line. It does not create a receipt, transaction, grade, or stored record. Copy result and Copy tape require a user gesture and report whether clipboard access succeeded.

Use CE, C, and Backspace deliberately

Backspace removes the final character, which is useful for a mistyped digit or operator. CE attempts to remove the numeric token around the active cursor and leaves the surrounding expression. If the cursor is not inside a number, CE returns a clear “No current numeric entry” notice. C clears the active line, result, and parse error while preserving earlier tape lines and the memory register.

These behaviors are part of this product, not claims about every calculator. The labels remain visible, tooltips repeat the scope, and keyboard shortcuts cannot override browser or assistive-technology commands.

Work with one volatile register

M+ adds the current valid result to memory. M− subtracts it. MR inserts the current register as a parenthesized decimal or exact rational literal that the same parser accepts. MC clears the register. If no valid result exists, M+ and M− do nothing and announce why.

The register begins at zero and has no named slots. It is not shared across tabs, tools, sessions, or devices. Refreshing the page clears it. A visible “Memory: 0” state prevents the mere presence of an M indicator from implying a saved value.

Read errors at the character position

For 4 + (3 × ), the parser stops after × and highlights the position where a primary value was expected. For 8 ÷ 0, syntax succeeds but the calculation returns a division-by-zero domain error. For 1.2.3 + 4, tokenization identifies the second decimal point.

The page does not guess that missing content should be zero or multiplication. Error messages name the unexpected token, expected category, and index. The expression remains editable, and focus stays in the input unless the user chooses another control.

Rational values and display rounding

Each finite decimal token becomes an integer coefficient over a power of ten. Operations reduce numerator and denominator with a greatest-common-divisor routine. A terminating result displays without unnecessary trailing zeros. A repeating result shows an exact fraction and a decimal rounded to at most 12 places under the declared half-away-from-zero display rule.

The display boundary is not a claim that 12 places fit every real-world problem. The input has caps on characters, tokens, grouping depth, and BigInt size. Errors are explicit when those boundaries are reached.

Calculator questions

Type a bounded expression and select Evaluate and add the line to the tape. Inspect the normalized syntax, result, exact form, and order summary. Correct any highlighted position, then copy only the line you intend to use elsewhere.