Percentage Calculator
Percentage calculator
Solve basics, changes, and comparisons fast.
Question type
Quick presets
Result
75%
45 is 75% of 60.
Status
Live
Context
Basics
Precision: 2 decimals
Formula and calculation steps
\text{Percentage}=\frac{\text{Part}}{\text{Whole}}\times100- 1.45 / 60 = 0.75
- 2.Multiply by 100 = 75%
Formula
Percentage = (Part / Whole) x 100 \text{Original} = \frac{\text{Final}}{1 \pm \text{Percentage}/100} \text{Percentage Difference} = \frac{|a-b|}{(|a|+|b|)/2} \times 100 Symbol legend
| Symbol | Meaning | Unit | Copy |
|---|---|---|---|
\text{Percentage} | Computed percentage value | % | |
\text{Part} | Observed or partial value | same as Whole | |
\text{Whole} | Reference total value | same as Part | |
\text{Original} | Value before an increase or decrease | same as Final | |
a,b | Two values being compared | same unit |
- Basic percentage questions rearrange the same part, whole, and percentage relationship.
- Reverse change divides the final value by the increase or decrease factor instead of subtracting the displayed percent.
- Percent change uses the original value as its baseline; percentage difference uses the average magnitude of both values and is order-independent.
Example
Worked example: reverse a 20% discount
- 1 Final value = 80
- 2 Decrease factor = 1 - 20/100 = 0.8
- 3 Original value = 80 / 0.8 = 100
A final value of 80 after a 20% decrease came from an original value of 100.
How
- Choose Basics, Change, or Compare.
- Select the question or solve direction, then enter the visible values.
- Read the live result and open Formula and calculation steps only when you need the working.
Avoid
- Swapping part and whole values, which reverses the ratio.
- Subtracting 20% from a discounted final value instead of dividing by the remaining 80% to find the original.
- Treating percent change and percentage difference as the same calculation.
- Reporting percentage points as percentage change when comparing two percentage values.
FAQ
How do I find a percentage, a part, or the whole?
Use Percentage = Part / Whole x 100, then rearrange it for the unknown value. The Basics tab exposes all three forms.
How do I find the original value before an increase or discount?
Divide the final value by 1 plus the increase rate, or by 1 minus the decrease rate. Use Change, then Find original.
What is the difference between percent change and percentage difference?
Percent change is directional and uses the original value as the baseline. Percentage difference is order-independent and compares the absolute gap with the average magnitude of both values.
Why is percent change from zero undefined?
The formula divides by the original value. When that value is zero there is no finite percentage baseline, although the absolute and symmetric differences can still be shown.
Switch
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