Percentage Calculator Manual

Choose the right mode

• Percent of a number: What is X% of Y?
• What percent?: X is what percent of Y?
• Increase / decrease: Apply a percentage adjustment to a starting value.
• Percentage change: Compare an Original value to a New value.
• Percentage difference: Compare two peer values when neither is the baseline.

Percent of a number

Result = Number × Percentage ÷ 100. Number is the amount you are taking a percentage of; Percentage is the rate. Both inputs may be signed. For example, 200 × 15 ÷ 100 = 30, so 15% of 200 is 30.

What percent?

Percentage = Part ÷ Whole × 100. Part is the amount being compared and Whole is the reference amount. Both may be signed, but Whole cannot be zero. For example, 30 ÷ 120 × 100 = 25%.

Increase / decrease

Increase result = Base × (1 + Percentage ÷ 100). Decrease result = Base × (1 − Percentage ÷ 100). Base is Starting value. Both inputs must be non-negative. Increase is selected initially.

The signed Change amount is Base × Percentage ÷ 100 for Increase, or its negative for Decrease. Increasing 250 by 12% gives 280, a change of 30; decreasing it by 12% gives 220, a change of −30. Percentages may exceed 100: decreasing 100 by 150% gives −50.

Percentage change

Percentage change = (New − Original) ÷ Original × 100. Original is the starting baseline and must be greater than zero. New value must be non-negative. The result is directional: positive means increase, negative means decrease, and zero means no change.

The signed Absolute change is New − Original. From 80 to 100, the absolute change is 20 and the percentage increase is 25%. From 100 to 80, it is −20 and a 20% decrease. Divide by Original, not New. Negative baselines are outside this app's scope.

Percentage difference

Percentage difference = |A − B| ÷ ((A + B) ÷ 2) × 100. The vertical bars mean absolute difference. Mycelgrid uses this average-denominator convention; percentage difference can be defined differently in other fields.

Value A and Value B must be non-negative and cannot both be zero. Neither value is the baseline, so swapping them preserves the result and no increase/decrease direction applies. For 50 and 75, the difference is 25, the average is 62.5, and the result is 40%. For 0 and 10, the result is 200%.

Input rules and zero denominators

Use ordinary decimal notation with digits before the decimal point, up to 30 numeric digits total and 12 fractional digits. Leading and trailing whitespace is ignored. Exponent notation, grouping commas, a plus prefix, interior spaces, NaN, and Infinity are rejected. Signed zero is normalized to zero in the two signed modes.

Whole cannot be zero in What percent?. Original must be greater than zero in Percentage change. Two zero values are undefined in Percentage difference because their average denominator is zero. These cases show a field error and clear the old answer; they never become Infinity or 0%. Incomplete inputs show a neutral placeholder.

Precision and the approximation marker

Inputs and calculations use exact decimal/rational arithmetic. A terminating result through 12 decimal places is displayed exactly unless its length requires scientific notation. Other ordinary-decimal results are rounded to at most 6 decimal places. Rounding uses half-up on the absolute magnitude, then reapplies the sign; exact ties round away from zero.

Tiny non-zero answers that would round to zero, and answers too long for the display, use scientific notation with up to 6 significant digits. A rounded value is marked ≈; an exact scientific representation needs no approximation marker. For example, 1% of 0.000001 is exact 0.00000001, while 1 out of 3 is ≈ 33.333333%. The calculation receipt keeps the normalized input values.

Copy result, Use example, and Reset

Copy result copies only the active valid calculation: its mode, normalized inputs, result, meaning, formula, substituted values, and applicable convention or approximation note. It does not copy drafts from other modes. Copy is disabled while the result is incomplete or invalid. If clipboard access fails, a selected text box lets you copy manually.

Use example fills the selected mode with its worked example. Replacing existing values asks for confirmation. Reset also asks before clearing meaningful values and clears only the active mode. Cancel keeps the current work.

Common mistakes and separate calculator jobs

Percentage change uses Original as the denominator; percentage difference uses the average here and is symmetric. Moving from 40% to 50% is 10 percentage points, but a 25% relative increase. Increasing 100 by 50% and then decreasing 150 by 50% gives 75 because the baseline changed.

This is a general mathematical calculator. Dedicated Percent Off, Percent Error, Margin, Markup, body/weight, tax, tip, payroll, finance, and grade-conversion workflows have additional rules beyond these five modes. A separate percentage-points mode and negative-baseline percentage change are not included. See Percentage Change vs Percentage Difference for the denominator comparison.

Local page memory

Switching modes keeps their drafts only in this browser page. The calculator does not upload entered numbers, save a calculation history, or offer account/cloud recovery. Refreshing or closing the page can discard the work. Navigation with meaningful work lets you open the destination in a new tab while keeping this calculation here, or leave this page. Share App shares only the app URL, never your calculation.