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Percentage Change: Increase & Decrease

Percentage change = ((new-old)/old)×100. Positive = increase, negative = decrease. Base is always the old value. Successive changes don't simply add.

Concept Fundamentals
((new-old)/old)×100
Change
new > old
Increase
new < old
Decrease
old (denominator)
Base

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Base is old value. 100→125 is 25% increase. 100→80 is 20% decrease. 80→100 is 25% increase (base 80). Successive 10%+10% ≠ 20%; it's 21% (1.1×1.1-1).

Key quantities
((new-old)/old)×100
Change
Key relation
new > old
Increase
Key relation
new < old
Decrease
Key relation
old (denominator)
Base
Key relation

Ready to run the numbers?

Why: Percentage change measures growth or decline: sales, population, prices, grades. Finance uses it for returns. Successive changes compound, not add.

How: ((new-old)/old)×100. Old cannot be zero. For successive changes: apply each to the updated value. 10% then 10% is not 20% total.

Base is old value. 100→125 is 25% increase.100→80 is 20% decrease. 80→100 is 25% increase (base 80).
Sources:NCTM StandardsKhan Academy

Run the calculator when you are ready.

Calculate Percentage ChangeEnter old and new values

Enter Values

pct-change.sh
CALCULATED
$ ./pct-change --old 100 --new 120
% Change
20% ↑
Absolute
20
Direction
Increase
Final
120
Percentage Change Calculator
20% Increase
From 100 to 120
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Values Comparison

Old vs New

📐 Step-by-Step Breakdown

SETUP
Step 1
Difference = 120 - 100 = 20
METHOD
Step 2
% Change = (20 / 100) × 100 = 20%
RESULT
Result
20% Increase

For educational and informational purposes only. Verify with a qualified professional.

🧮 Fascinating Math Facts

%

((new-old)/old)×100

— Percentage change

↗

Increase: new > old

— Positive change

📋 Key Takeaways

  • • Percentage Change = ((new − old) / old) × 100
  • • Positive result = increase; negative = decrease
  • • Initial value cannot be zero (division by zero)
  • • 50% increase then 50% decrease does not return to start (100 → 150 → 75)
  • • Successive changes compound: each % applies to the new base

💡 Did You Know?

📊Percentage point vs %: 10% to 15% is +5 pp, but +50% relative changeSource: Distinction
⚡A 100% increase doubles the value; 100% decrease goes to zeroSource: Limits
🔄Successive 10% + 10% on 100 gives 121, not 120Source: Composition
📐Used in finance: stock returns, inflation, sales growthSource: Applications
✓Symmetry: 50% up then 50% down = 25% net decreaseSource: Asymmetry
📉Maximum decrease is 100% (value becomes zero)Source: Bound

📖 How It Works

Enter the initial (old) value and final (new) value. The calculator computes (new − old) / old × 100. In Advanced mode, you can apply successive percentage changes (e.g., 10, -5, 20) to see the compounded effect. Each change applies to the current value, not the original.

📝 Worked Example: 100 to 120

Step 1: Difference = 120 − 100 = 20

Step 2: % Change = (20 / 100) × 100 = 20%

Result: 20% increase

Verification: 100 × 1.20 = 120 ✓

🚀 Real-World Applications

📈 Stock Returns

Daily, monthly, yearly price changes.

💰 Inflation

CPI, cost-of-living adjustments.

🛒 Sales & Discounts

Price changes, markdowns.

📊 Business KPIs

Revenue growth, conversion rates.

🏥 Health Metrics

Weight change, lab value trends.

📉 Population

Demographic growth/decline.

⚠️ Common Mistakes to Avoid

  • Wrong base: Always divide by the original value, not the new one.
  • Adding successive %: 10% then 10% ≠ 20%. Multiply: 1.1 × 1.1 = 1.21 (21%).
  • Confusing pp and %: 10% to 15% is +5 percentage points, +50% relative.
  • Assuming symmetry: 50% up then 50% down leaves you at 75% of start.
  • Zero initial: Division by zero is undefined. Use absolute change.

🎯 Expert Tips

💡 Base Matters

Always divide by the original value, not the new one.

💡 Successive Changes

10% then 10%: multiply by 1.1 twice = 1.21 (21% total).

💡 Absolute vs Relative

$10 to $20 is 100% increase; $100 to $110 is 10%.

💡 Reverse Calculation

New = Old × (1 + p/100). Old = New / (1 + p/100).

📊 Reference Table

ScenarioFormula
Basic % change((new - old) / old) × 100
Absolute changenew - old
Find new from %new = old × (1 + p/100)
Find old from newold = new / (1 + p/100)

📐 Quick Reference

100%
Doubles value
50%
Half increase
-100%
Goes to zero
0%
No change

🎓 Practice Problems

80 to 100 → Answer: 25% increase
200 to 150 → Answer: 25% decrease
100 +10% then +10% → Answer: 121 (21% total)
50 to 75 → Answer: 50% increase

❓ FAQ

What is percentage change?

((new − old) / old) × 100. Measures relative change from original.

Why can initial value not be zero?

Division by zero is undefined. Report absolute change instead.

50% up then 50% down back to start?

No. 100 to 150 to 75. Each % applies to new base.

Percentage point vs percent?

10% to 15% is +5 percentage points. Relative change is 50%.

How do successive changes work?

Apply each % to current value: 100 +10% = 110, +10% = 121.

When is it increase vs decrease?

Positive % = increase (new > old). Negative % = decrease.

How do I find new value from % increase?

New = Old × (1 + p/100). E.g. 100 + 20% = 100 × 1.20 = 120.

📌 Summary

Percentage change = ((new − old) / old) × 100. Always use the original value as the base. Successive changes compound. Distinguish percentage points from percent change. Use for finance, growth metrics, and trend analysis.

✅ Verification Tip

For p% increase: New = Old × (1 + p/100). Check: if 20% increase from 100, then 100 × 1.20 = 120. For decrease, use (1 − p/100).

🔗 Next Steps

Explore the Percentage Calculator for x% of y, the Decimal to Percent Calculator for conversions, and the Percentage Error Calculator for measurement accuracy.

⚠️ Disclaimer: For educational use. Verify financial calculations with professionals.

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