How to Work Out a Percentage of 2 Numbers: Step-by-Step Guide

So you need to figure out a percentage? Maybe it's for a test, maybe it's for splitting a restaurant bill fairly after that awkward dinner with friends, or perhaps you're trying to understand if that "50% off!" sale sign is actually a good deal. Whatever the reason, knowing how to work out a percentage of 2 numbers is one of those basic math skills that pops up way more often than you'd think.

Honestly, I used to dread percentage calculations. Back in school, it felt abstract and pointless. Then I started budgeting, comparing phone deals, figuring out recipe adjustments, and even tracking my running progress – suddenly, percentages were everywhere! That mental block? Gone. It's genuinely easier than it seems at first glance.

Let's cut through the jargon and get straight to the practical stuff. This guide isn't about memorizing textbooks; it's about giving you the tools to solve real problems right now.

The Absolute Core: The Percentage Formula (It's Easier Than You Think)

Forget complicated theories. The core formula for finding **what percentage one number is of another number** is refreshingly simple:

That's it. Seriously. This little formula unlocks almost everything you need to know about how to work out a percentage between two numbers. Let's break down what those words mean:

• Part: This is the smaller piece you're interested in. (e.g., The discount amount taken off a shirt, the number of questions you got right on a quiz, the profit you made this month).
• Whole: This is the total or the complete amount. (e.g., The original price of the shirt, the total number of questions on the quiz, your total revenue for the month).
• * 100: This converts the decimal result you get from (Part / Whole) into an actual percentage. Without multiplying by 100, 0.25 is just a decimal. Multiply by 100, it becomes 25% – much more meaningful!

Think of it like slicing a pie. The "Whole" is the entire pie. The "Part" is the slice you're looking at. The percentage tells you what fraction of the whole pie your slice represents, scaled up to be out of 100 slices.

Your Step-by-Step Blueprint (With Real Examples)

Let's turn that formula into actionable steps. Grab a calculator (your phone's is fine!) or a pen and paper. Here’s exactly what to do:

Step 1: Identify Your "Part" and Your "Whole"

This is the most crucial step and where people sometimes trip up. Ask yourself: "What am I trying to find the percentage OF?" That answer is your Whole. Then ask: "What specific portion am I measuring?" That's your Part.

Scenario: You scored 42 marks out of a possible 60 on your Math test. What percentage is that?

• What's the total possible? 60 marks. That's your Whole.
• What did you actually score? 42 marks. That's your Part.

Scenario: Your energy bill last month was $125. This month it's $98. You want to know the percentage decrease.

• What's the original amount? $125 (Last month). That's your starting point, often the Whole when calculating change.
• What's the change amount? $125 - $98 = $27 saved. This $27 is the Part (the decrease amount in this context).

Step 2: Divide the Part by the Whole

Take the Part number and divide it by the Whole number.

Test Example: Part (42) / Whole (60) = 42 ÷ 60 = 0.7

Bill Example: Part ($27 decrease) / Whole ($125 original) = 27 ÷ 125 = 0.216

Step 3: Multiply the Result by 100

This transforms your decimal into a recognizable percentage.

Test Example: 0.7 * 100 = 70%

Bill Example: 0.216 * 100 = 21.6%

So, you scored 70% on your test, and you reduced your energy bill by 21.6% compared to last month! See? Not so scary.

Beyond the Basics: Different Flavors of Percentage Problems

Life isn't always about finding what percentage one number is of another. Sometimes you know the percentage and need to find the actual value. Let's cover those common variations.

Finding the Part When You Know the Whole and the Percentage

Formula: Part = (Percentage / 100) * Whole

Scenario: You're leaving a 15% tip on a restaurant bill of $85. How much is the tip amount?

• Percentage = 15%
• Whole = $85 (The total bill before tip)
• Part (Tip Amount) = (15 / 100) * $85 = 0.15 * $85 = $12.75

Finding the Whole When You Know the Part and the Percentage

Formula: Whole = Part / (Percentage / 100)

Scenario: You see a jacket on sale for $63. The sign says it's 30% off. What was the original price?

• Percentage = 30% OFF. Important! The sale price ($63) represents 100% - 30% = 70% of the original price.
• Part = $63 (This is 70% of the original)
• Whole (Original Price) = Part / (Percentage / 100) = $63 / (70 / 100) = $63 / 0.70 = $90

This one trips people up a lot – forgetting that the sale price is a percentage *of* the original, not the discount itself. Be careful!

Handling Tricky Situations (Zero, Negatives, Big Percentages)

The core formula works most of the time, but what about edge cases?

Why Getting Percentages Right Actually Matters (Beyond the Math Test)

This isn't just academic. Messing up percentages can cost you money or lead to bad decisions:

• Personal Finance: Calculating interest on loans (APR%) or savings (APY%), understanding credit card fees, calculating discounts accurately during sales, figuring out tax rates (e.g., VAT, Sales Tax), budgeting allocations.
• Health & Fitness: Tracking weight loss/gain (% of body weight), calculating body fat percentage goals, understanding nutrition labels (% Daily Value), measuring workout progress (e.g., % increase in weights lifted).
• Shopping: Comparing deals effectively ("Is 30% off one item better than 'Buy One Get One 50% Off'?"), calculating final prices after discounts and taxes.
• Work & Business: Calculating profit margins, sales commission, performance increases/bonuses, market share statistics, project completion percentages, data analysis in spreadsheets.
• Statistics & News: Understanding polls, surveys, risk assessments ("a 20% increased chance"), inflation rates, economic growth figures.

I remember confidently telling a friend a "huge" 50% discount I found on a gadget I wanted. He calmly asked, "50% off what?" Turned out the original price was massively inflated, and competitors were selling it for the same "sale" price without any discount! Knowing how to work out a percentage of 2 numbers helps you see through the marketing spin.

Common Pitfalls & How to Dodge Them

Even with the formula, mistakes happen. Here's where people often slip up:

Pitfall 1: Mixing Up "Part" and "Whole"

This is the big one. Are you finding what percentage OF the total something is? Or are you finding a value that IS a certain percentage OF the total?

• Fix: Always ask: "What is the complete amount here?" That's your Whole. "What specific piece of that whole am I focusing on?" That's your Part.

Pitfall 2: Forgetting the "* 100"

You divide Part by Whole, get 0.35, and confidently declare the answer is 0.35. Oops! You forgot to convert to a percentage.

• Fix: That "* 100" is non-negotiable. Make it a habit. Mentally shout "MULTIPLY BY ONE HUNDRED!" after your division.

Pitfall 3: Misinterpreting Percentage Change

Calculating the percentage change from an old value to a new value requires finding the difference first.

Correct Formula for % Change: ((New Value - Old Value) / |Old Value|) * 100
(The absolute value |Old Value| prevents issues when Old Value is negative, but usually we use the positive value).

Scenario: Your investment grew from $1,000 to $1,200.

• Difference = $1,200 - $1,000 = $200
• % Increase = ($200 / $1,000) * 100 = 20%

Pitfall 4: Confusing Percentage Points with Percentages

This is huge in finance and news. A percentage point is simply a unit of 1%.

• If an interest rate increases from 5% to 7%, it has increased by 2 percentage points.
• However, it has increased by (2 / 5) * 100 = 40% (relative percentage increase).

News might say "Interest rates jumped 40%!" (technically true relative to the old rate) when the actual increase is 2 percentage points. Knowing the difference helps you understand the real scale.

Tools & Shortcuts: When to Use Them (And When Not To)

While understanding the formula is essential, tools can speed things up:

• Built-in Calculator Apps (iPhone, Android, Windows): Almost always have a percentage (%) button. Learn how it works on your specific device – it usually assumes the number entered before it is the percentage you want to apply to the number currently displayed. Test it with simple cases (e.g., 100 + 10% should = 110).
• Spreadsheets (Google Sheets, Microsoft Excel): The powerhouse for percentages. Use formulas like:
  • =A1/B1 (Gives decimal, format cell as '%' or multiply by 100)
  • =A1/B1 * 100 (Explicitly gives percentage number)
  • =(B1-A1)/ABS(A1) (Percentage change)
• Online Percentage Calculators: Convenient for quick checks. Search "percentage calculator." Reputable ones include Calculator.net's Percentage Calculator or Omni Calculator's Percentage tools. But: Don't rely solely on these without understanding – they won't help you identify your Part and Whole correctly.
• Mental Math Tricks:
  • 10%: Just move the decimal point one place left. ($85 -> $8.50 is 10%).
  • 5%: Find 10% and then halve it. ($85 -> $8.50 / 2 = $4.25).
  • 20%: Find 10% and double it. ($85 -> $8.50 * 2 = $17.00).
  • 50%: Just divide by 2. ($85 / 2 = $42.50).
  • 25%: Divide by 4 (or find 50% and halve it). ($85 / 4 = $21.25).
  Combine these for others (e.g., 15% = 10% + 5% = $8.50 + $4.25 = $12.75 on $85).

While that fancy financial calculator app might look impressive, honestly, your phone's basic calculator combined with these mental tricks covers 95% of daily needs. Don't overcomplicate it.

Putting It All Together: Real-World Scenarios Solved

Let's tackle some common situations where you need to work out a percentage of two numbers:

Scenario 1: The Restaurant Tip

• Situation: Bill is $78.50. Service was good, you want to leave 18%.
• Task: Find the tip amount.
• Approach: Part = ? (Tip), Whole = $78.50, Percentage = 18%.
  • Part = (18 / 100) * $78.50 = 0.18 * $78.50
  • Calculate: 0.18 * 70 = 12.60, 0.18 * 8.50 = 1.53, Total Tip = $14.13
  • Mental Math Check: 10% = $7.85, 5% ≈ $3.93, 2.5% ≈ $1.96. 18% = 10% + (5% * 1.6) ≈ $7.85 + ($3.93 * 1.6). Round: $3.93*1.6 ≈ $6.29, Total ≈ $7.85 + $6.29 = $14.14 (Close enough!).

Scenario 2: Understanding a Salary Increase

• Situation: Old salary $52,000/year. New offer $58,500/year. What's the percentage increase?
• Task: Find the % increase.
• Approach:
  • Difference = $58,500 - $52,000 = $6,500
  • % Increase = ($6,500 / $52,000) * 100
  • Calculate: $6,500 / $52,000 ≈ 0.125 * 100 = 12.5%

Scenario 3: Sale Price Confusion

• Situation: A dress is marked "40% off." The sale price is $72. What was the original price?
• Task: Find the Whole (Original Price).
• Approach: The sale price ($72) is what you pay AFTER 40% off. So $72 represents (100% - 40%) = 60% of the original price.
  • Part = $72 (60% of original)
  • Whole (Original Price) = Part / (Percentage / 100) = $72 / (60 / 100) = $72 / 0.60 = $120
• Check: 40% of $120 = $48 off. $120 - $48 = $72. Correct!

Answers to Your Burning Percentage Questions (FAQ)

Let's clear up some common confusions people have when trying to work out a percentage between two numbers:

How do I calculate percentage increase or decrease?

Use the percentage change formula:

• % Change = [(New Value - Old Value) / |Old Value|] * 100
• If the result is positive, it's an increase.
• If the result is negative, it's a decrease.
• Example (Decrease): Stock price dropped from $80 to $68.
  • Difference = $68 - $80 = -$12
  • % Change = [-$12 / $80] * 100 = -0.15 * 100 = -15% (A 15% decrease).

What's the difference between "percent" and "percentage points"?

This is vital, especially in finance and statistics:

• Percent (%): A proportion out of one hundred relative to a base value.
• Percentage Point: A simple arithmetic difference between two percentages.
• Key Distinction: If a bank raises its interest rate from 3% to 4%, that's:
  • A rise of 1 percentage point (4% - 3% = 1).
  • A relative increase of (1 / 3) * 100 ≈ 33.3% (from the original 3% base).
  News might say "Interest rates surged 33%!" (referring to the relative change) which sounds huge, but the actual practical difference is only 1 percentage point. Always check the context!

How do I add or subtract a percentage?

Adding:

• Method 1: Find the percentage amount and add it to the original.
  • Original Price: $200, Add 8% Tax: (8/100)*$200 = $16, Total = $200 + $16 = $216.
• Method 2: Use a multiplier: Original * (1 + (Percentage/100))
  • $200 * (1 + 0.08) = $200 * 1.08 = $216.

• Method 1: Find the percentage amount and subtract it from the original.
  • Original Price: $200, 15% Off: (15/100)*$200 = $30, Sale Price = $200 - $30 = $170.
• Method 2: Use a multiplier: Original * (1 - (Percentage/100))
  • $200 * (1 - 0.15) = $200 * 0.85 = $170.

Can a percentage be more than 100%?

Absolutely! It just means the "Part" is larger than the "Whole" you are comparing it to. This is common in growth situations:

• "Our sales this quarter are 150% of last quarter's sales." (Meaning sales are 1.5 times larger).
• "She gave 110% effort." (Figuratively meaning more than the maximum expected).

How do I calculate a percentage of a percentage?

This usually means applying one percentage to the result of another percentage. Be careful with order!

• Scenario: You get a 10% discount on an item, and then an additional 5% discount at the register on the discounted price. How much do you pay for a $100 item?
• Step 1: Apply first discount: $100 * (1 - 0.10) = $100 * 0.90 = $90.
• Step 2: Apply second discount to the new price: $90 * (1 - 0.05) = $90 * 0.95 = $85.50.
• Is it the same as 15% off? 15% off $100 is $85. $85.50 is slightly more. Why? Because the 5% is taken off the already reduced $90, not the original $100.

What tools are best for complex percentage calculations?

For anything beyond simple daily math, spreadsheet software like Microsoft Excel or Google Sheets is unbeatable. They handle complex chains of percentages, percentages of percentages, and large datasets effortlessly using formulas. Financial calculators (like the HP 10bII+, around $30-$40) are designed specifically for finance-related percentage calculations (interest, amortization, etc.) but are overkill for most everyday needs.

Final Thoughts: Mastering the Skill

Understanding how to work out a percentage of 2 numbers isn't about complex algebra; it's fundamentally about identifying three things: the Part, the Whole, and the Percentage you know or need to find. Get those three elements clear in your mind, plug them into the right variation of the core formula (Percentage = Part/Whole * 100, Part = (Percentage/100)*Whole, Whole = Part / (Percentage/100)), and you're almost there.

The real skill comes with practice and applying it to situations that actually matter to you. Calculate the tip on your next meal mentally. Figure out the real discount percentage on that sale item before you buy. Track the percentage of your monthly budget spent on coffee (it might be scary!).

Don't be afraid to double-check with a calculator, especially for important stuff like finances. And remember the pitfalls – mixing up Part and Whole or forgetting the *100 are the classic stumbles, and confusing percentage points with percentages can lead to misinterpreting important information.

Math anxiety around percentages is really common, but once you break it down step-by-step with practical examples, the fog lifts. It becomes a genuinely useful tool, not a chore. You've got this!