Percentages
Percentage increase or decrease, percentage points versus percent, converting a decimal to a percent, and slope expressed as a percentage grade: one of the most-searched math subcategories on the site.
Calculators & Tools
Percentage Increase Calculator
Calculates percentage increase in three modes: find the new value after a percentage rise, find what percentage one value increased relative to another, or reverse-engineer the original value before a known percentage increase. Includes step-by-step working and edge-case warnings for zero and negative inputs.
Percentage Calculator
This percentage calculator covers all five core percentage problems: finding a percentage of a number, what percent one number is of another, reverse percentage to find the original value, percentage change between two values, and percentage difference. Each result shows step-by-step working so you can verify your answer or learn the method.
Percent Error Calculator
Calculates percent error between an observed and a true value, with a toggle for signed or absolute output. Reverse modes calculate the possible observed value from a known true value and percent error, or the possible true value from a known observed value and percent error, returning two candidate answers since an unsigned error does not reveal direction. Distinguishes percent error from percent difference and percent change.
Percentage Change Calculator
The Percentage Change Calculator measures how much a value has increased or decreased between two points, expressed as a percentage of the original value. It works in three modes: finding the % change between two numbers, applying a known % change to find a new value, and reversing a % change to recover the original. Negative starting values and sign-crossing changes are flagged with explanatory notes.
Time Percentage Calculator
Calculates the percentage of a total time period that has elapsed, using three methods: comparing a part duration against a total duration in hours and minutes, tracking progress through a work shift by clock time (with automatic handling of shifts that cross midnight), or tracking progress through a calendar date range such as a project timeline or fiscal year.
Percentage Point Calculator
Calculates the percentage point difference between two rates, converts the result to basis points (1 percentage point = 100 bps), and shows the equivalent relative percentage change for comparison. Also applies a known percentage point change to a starting rate, or reverse-engineers a possible second rate from a known rate and a percentage point gap. Distinguishes percentage points from percentage change.
Percentage Decrease Calculator
Calculates percentage decrease in three modes: find the new value after a percentage reduction, find what percentage one value fell relative to another, or reverse-engineer the original value before a known percentage decrease. Includes step-by-step working and edge-case warnings for zero, 100%, and negative inputs.
Percent to Goal Calculator
Calculates the percentage of a goal reached (current value divided by goal value), the daily pace required to close the remaining gap by a set deadline, or the current value that corresponds to a target percentage. Applies to sales quota attainment, fundraising campaigns, savings goals, fitness targets, and project tracking, with an industry benchmark note that sales attainment above 80% is generally considered solid.
Percentage Difference Calculator
Calculates the percentage difference between two values (a symmetric comparison using their average as the denominator) or reverse-engineers the two possible values that would produce a known percentage difference from a given starting value. Distinguishes percentage difference from percentage change and percentage error, since the three use different denominators and answer different questions.
Slope Percentage Calculator
Converts slope between three standard formats: percentage grade (rise/run x 100), angle in degrees (arctangent of the percentage), and ratio (1 in N). Accepts input starting from any of the three formats and computes the other two, along with a roof pitch equivalent and an ADA ramp compliance check against the 8.33% (1:12) accessibility maximum. Flags the common misconception that a 100% grade equals 45 degrees, not vertical.
Average Percentage Calculator
Calculates the average of multiple percentages using three methods: a simple unweighted average for equal sample sizes, a weighted average that accounts for differing sample sizes, or a raw-numbers method that sums the original numerators and denominators before converting to a single overall percentage. Warns when sample sizes vary significantly enough that a simple average would be misleading.
Decimal to Percent Converter
Converts between decimal, percentage, and fraction formats in either direction: decimal to percent (multiply by 100), percent to decimal (divide by 100), or fraction to both simultaneously. Flags a warning about the common spreadsheet formatting confusion, where a cell displaying a percentage may already store the underlying decimal value, leading to accidental double-conversion errors.
Doubling Time Calculator
Calculates doubling time using both the Rule of 72 shortcut and the exact logarithmic formula side by side, so users can see how closely the two agree for a given growth rate. Also calculates the growth rate required to hit a target doubling time, and generalises the doubling calculation to any custom multiple (tripling, quadrupling, or other multiples) of a starting value.
Percentage of a Percentage Calculator
Calculates percentage of a percentage in two distinct senses: a simple multiplication (X% of Y%, such as 10% of 20% equalling 2%) and stacked or sequential discounts applied one after another to a value, where the combined effective discount is always less than the naive sum of the individual percentages. Also reverse-calculates a missing discount from a known combined effect and one known discount.