Percentage Calculator
Four essential percentage tools in one place. All calculations run instantly in your browser - nothing is sent to any server.
Find the value that a given percentage represents of a number.
What is a Percentage?
A percentage is a number or ratio expressed as a fraction of 100. The word comes from the Latin per centum, meaning "by the hundred." When you write 45%, you are saying 45 out of every 100, or equivalently the fraction 45/100 = 0.45.
Percentages are the universal language of proportions. They appear in finance (interest rates, returns), science (concentrations, statistics), everyday shopping (discounts, tax), and data analysis. Because they normalise everything to a common scale of 0-100, they make it easy to compare quantities that would otherwise be measured in completely different units or magnitudes.
Percent of a Number
The most fundamental percentage question: "What is X% of Y?" To find a percentage of a number, convert the percentage to its decimal equivalent (divide by 100) and multiply by the number.
Formula
Result = (Percentage / 100) × Number Example: What is 15% of 80? Answer: (15 / 100) × 80 = 0.15 × 80 = 12.
Common uses include calculating a tip at a restaurant (15-20% of the bill), working out VAT or sales tax added to a price, finding how much of a budget a single line item consumes, or determining the weight of an ingredient in a recipe expressed as a proportion of total weight.
Percent Change
Percent change measures how much a value has grown or shrunk relative to its original value. It is directional: a positive result is an increase, a negative result is a decrease.
Formula
Percent Change = ((New - Original) / |Original|) × 100 Example: A stock price moves from $80 to $100. Percent change = ((100 - 80) / 80) × 100 = +25% increase.
Reverse example: A stock price drops from $100 to $80. Percent change = ((80 - 100) / 100) × 100 = -20% decrease. Notice that a 25% gain does not cancel a 20% loss - they are calculated against different baselines.
Percent change is used wherever tracking growth over time matters: year-over-year revenue figures, population growth rates, portfolio performance, website traffic trends, and scientific measurements comparing an experimental value to a baseline.
Percent Difference
Percent difference answers the question: "How different are these two values from each other?" Unlike percent change, it has no direction - there is no "original" and "new." Both values are treated equally, and the reference point is their average.
Formula
Percent Difference = (|A - B| / ((A + B) / 2)) × 100 Example: Two sensors measure a temperature as 50°C and 75°C. Percent difference = (|50 - 75| / ((50 + 75) / 2)) × 100 = (25 / 62.5) × 100 = 40%.
This metric is common in scientific experiments comparing two independent measurements, in pricing comparisons between two competing products, and in quality control when neither measurement is considered the "true" reference value.
Ratio to Percent
A ratio expresses a part relative to a whole. Converting it to a percentage simply scales that relationship to a denominator of 100, making it instantly interpretable.
Formula
Percent = (Part / Whole) × 100 Example: A student scores 42 out of 60 marks. Percentage = (42 / 60) × 100 = 70%.
Ratio-to-percent conversions are used constantly: converting fractions to percentages for grading, expressing market share (a company holds 3 of 12 contracts = 25%), calculating completion rates in project management, expressing survey responses as proportions, and converting probability fractions to percentage likelihoods.
Percent Change vs. Percent Difference
These two concepts are frequently confused because they both compare two numbers and return a percentage. The critical distinction is context:
Percent Change
- One value is the starting point (original)
- The other is the ending point (new)
- Direction matters: increase or decrease
- Denominator is the original value
- Use for: growth rates, before/after comparisons
Percent Difference
- Both values have equal status
- No direction - always a positive result
- Denominator is the average of both values
- Use for: comparing two independent measurements
- Symmetric: swapping A and B gives the same result
Rule of thumb: If one value is a "before" and the other is an "after," use percent change. If you are comparing two peer measurements with no inherent order, use percent difference.
Quick Reference: Percentage Formulas
| Calculation | Formula | Example |
|---|---|---|
| Percent of number | (P / 100) × N | 20% of 150 = 30 |
| Percent change | ((New - Old) / |Old|) × 100 | 50 to 75 = +50% |
| Percent difference | |A - B| / avg(A, B) × 100 | 40 and 60 = 40% |
| Ratio to percent | (Part / Whole) × 100 | 3 of 4 = 75% |
Common Percentage Mistakes
Asymmetry of increases and decreases
A 50% increase followed by a 50% decrease does not return to the original value. If you start at 100, +50% gives 150, then -50% of 150 gives 75 - a net loss of 25%. This is because each percentage is calculated against a different base.
Percentage points vs. percentages
If an interest rate rises from 2% to 3%, it has increased by 1 percentage point, but by 50% in relative terms. These are very different statements. Percentage points describe an absolute difference between two percentages; percent change describes the relative growth.
Using percent change when percent difference is appropriate
When comparing two thermometers, two lab results, or two parallel survey responses, neither value is the "original." Using percent change would arbitrarily privilege one measurement over the other and produce a different answer depending on which you call "original." Use percent difference instead.
Over 100% is valid
Percentages can exceed 100%. A 150% increase means the new value is 2.5 times the original. A ratio of 5/2 expressed as a percentage is 250%. "Over 100%" is not an error - it simply means the value has more than doubled relative to the reference.