Home - Math Calculators - Percentage Calculator – p% of x, What Percent, Increase/Decrease

Math Calculators

Percentage Calculator – p% of x, What Percent, Increase/Decrease

Aniruddh

September 8, 2025

38 Views

Everyday math shows up in bills, grades, profits, and dashboards. This Percentage Calculator turns those moments into quick answers you can trust. You pick a mode, enter numbers, and see the steps plus a clean result. No fluff. Just clear math that works on desktop and mobile.

Why this percentage calculator is different

You usually want answers first not theory. This tool gives you both.
Pick the mode you need, type your numbers, and copy the result. Then scroll for quick formulas, step-by-step examples, and a short FAQ. You’ll also find a precision guide and a cheat sheet you can bookmark.

How to use the four modes

1) p% of x

• Goal: find a part of a whole.
• Fields: Percent (p) and Base (x).
• Formula: result = x × (p ÷ 100)
• Example: 34% of 56 → 56 × 0.34 = 19.04

2) x is what % of y

• Goal: compare two numbers as a percent.
• Fields: x (part), y (whole).
• Formula: p = (x ÷ |y|) × 100
• Example: 30 is what percent of 120 → 30 ÷ 120 × 100 = 25%

3) x is p% of what?

• Goal: recover the whole when you know a part and the percent.
• Fields: x (part), p (percent).
• Formula: whole = x ÷ (p ÷ 100)
• Example: 10 is 10% of what → 10 ÷ 0.10 = 100

4) Increase / Decrease

• Goal: apply or reverse a percent change.
• Fields: Original, Percent, New.
• Formulas:
  • Increase: new = original × (1 + p ÷ 100)
  • Decrease: new = original × (1 − p ÷ 100)
  • Absolute change: Δ = new − original
  • Percent change from two numbers: p = |Δ| ÷ |original| × 100

Tip: Enter any two fields — the third fills in. If you type Original and New the calculator infers direction and percent.

Quick-reference table

Worked examples you can copy

These examples mirror the interface. Try them right in the calculator to check your understanding.

Example A: Tip at a restaurant

You want to leave 18% on a $46.50 bill.

• Mode: p% of x
• Input: p = 18, x = 46.50
• Calculation: 46.50 × 0.18 = 8.37
• Result: tip = $8.37 and total = $54.87

Example B: Test grade

You scored 34 points out of 40. What’s the percentage?

• Mode: x is what % of y
• Input: x = 34, y = 40
• Calculation: 34 ÷ 40 × 100 = 85
• Result: 85%

Example C: Original price from a discounted price

A jacket costs $72 after a 20% discount. What was the original price?

• Mode: x is p% of what?
• Input: x = 72, p = 80 if you think of 72 as 80% of original
  • Or keep p as 20 and use Increase/Decrease to reverse a decrease
• Calculation: 72 ÷ 0.80 = 90
• Result: original = $90

Example D: Salary raise

Your salary was $3,600. You received a 7.5% raise.

• Mode: Increase / Decrease → Increase
• Input: original = 3600, p = 7.5
• Calculation: 3600 × 1.075 = 3870
• Result: new = $3,870 and absolute change = $270

Example E: Price drop analysis

A phone fell from $999 to $799.

• Mode: Increase / Decrease
• Input: original = 999, new = 799
• The calculator infers a decrease and fills p = 20.02…
• Result: price went down about 20.02% and change = −$200

Precision and rounding (in simple terms)

Numbers rarely stay tidy. You’ll often meet repeating decimals or large totals. The calculator’s Rounding → Auto setting chooses a sensible number of decimals based on the size of the result so you get a clean answer that still reflects the input. If you need a fixed decimal count set it to 0–6 in the header.

When to change rounding:

• Reports that require exactly two decimals like financial statements
• Scientific notes that use four or more decimals
• Classroom work that asks for a specific precision

Tip: Rounding shows in the output only. Your internal math uses full precision to avoid compounding errors.

Common mistakes and how to avoid them

1. Forgetting to divide by 100
   Writing x × p instead of x × (p ÷ 100) blows up the result. Always convert a percent to its decimal form first.
2. Mixing percent change with percentage points
   Going from 8% to 10% is a 2 percentage-point increase not a 25% increase. The percent change is 2 ÷ 8 × 100 = 25%. See the table below for a quick comparison.
3. Using the wrong base for “what percent”
   In “x is what percent of y” the y is the whole not the difference.
4. Applying a discount twice
   A 25% discount followed by another 25% discount is not 50%. It’s price × 0.75 × 0.75 = price × 0.5625 so the combined discount is 43.75%.
5. Ignoring negative numbers in change
   The percent change formula uses absolute values for original and difference to prevent sign confusion. The calculator still tells you if the change is up or down.

Percentage vs percentage points

Use percent change when you compare scale. Use percentage points when you compare labeled rates.

Real-life use cases

• Shopping: find sale prices, stack discounts correctly, and compare savings between stores.
• Finance: compute fees, yields, or margin changes without pulling out a spreadsheet.
• School: check homework on ratios, tips, and percent word problems.
• Health: track body fat change or hydration targets with percent moves not raw differences.
• Business: report KPI deltas clearly so your team reads the same story you do.

Cheat sheet you can bookmark

Formulas at a glance

• part = base × (p ÷ 100)
• p = (part ÷ |whole|) × 100
• whole = part ÷ (p ÷ 100)
• new = original × (1 ± p ÷ 100)
• percent change = |new − original| ÷ |original| × 100

Mental-math shortcuts

• 10% of any number is just move the decimal one place left
• 5% is half of 10%
• 15% is 10% + 5%
• 25% is a quarter × 1
• 33⅓% is roughly one third
• 1% of x is x ÷ 100 then scale as needed

Mini-guide: select the right mode from the words

• “What is 18% of 72?” → p% of x
• “What percent is 18 of 72?” → x is what % of y
• “18 is 12% of what?” → x is p% of what
• “72 increased by 18%” or “72 decreased by 18%” → Increase/Decrease

When a sentence mixes hints use the nouns. Part and whole decide the mode every time.

Troubleshooting odd results

• I see many decimals. Set Rounding to a fixed number like 2. The math stays exact then the output formats cleanly.
• My copy includes commas. That’s fine for most apps. If you need plain digits use the “Copy” button then paste into a numeric cell which will strip formatting.
• 0 in the denominator warning. That means the “whole” can’t be 0 for that calculation. Fix the input or pick a different mode.

Frequently asked questions (clear and concise)

What is a percentage in one sentence?

A percentage expresses a part per one hundred which turns ratios into a common language.

How do I turn a number into a percent?

Multiply the decimal by 100 and add the % sign. Example: 0.375 × 100 = 37.5%.

How do I convert a percent to a decimal?

Divide by 100. Example: 8% becomes 0.08.

Is a 50% decrease the same as half price?

Yes. A 50% decrease multiplies the original by 0.5 which is half.

Why does “down then up” by the same percent not return to the start?

Percent changes apply to the current value not the original. Down 20% then up 20% → x × 0.8 × 1.2 = x × 0.96 which is still 4% lower.

What’s the difference between percent change and percentage points?

Percent change measures relative size. Percentage points measure absolute movement between two percentages.

Can I reverse a discount to find the original price?

Yes. Use x is p% of what with p as the remaining percent after the discount. Example: price after 25% off is 75% of original.

Does the calculator accept thousands separators or commas?

Yes. It understands both 1,200 and 1200 and it accepts 12,5 as 12.5 for international users.

Is this suitable for education or finance?

It works well for both. For audited reports set a fixed rounding level to match your house style.

Short glossary

• Percent (p): parts per hundred
• Base / Whole: the reference amount you compare to
• Part: the portion of the whole
• Percent change: relative movement between two values
• Percentage points: absolute difference between two percentages

References for deeper reading

• Introduction to percentages — Khan Academy: https://www.khanacademy.org/math/arithmetic/arith-review-percent
• Percentage point — Wikipedia: https://en.wikipedia.org/wiki/Percentage_point
• Percent change and growth — Wolfram MathWorld: https://mathworld.wolfram.com/PercentChange.html

Percent problems show up everywhere. You shop for deals, you measure progress, you explain reports. A good calculator gets out of your way and gives you answers in seconds. Keep this page bookmarked. Use the quick-reference table when you’re in a rush then dig into the examples if any step feels fuzzy. With these four modes locked in you’ll handle any percentage task with confidence.