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Percentage Decrease

Calculate the value after a percentage decrease, find the percentage decrease between two values, or model successive decreases over time with depreciation schedules and half-life.

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Why: Understanding percentage decrease helps you make better, data-driven decisions.

How: Enter Original Value, Percentage Decrease (%), Decreased Value to calculate results.

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Quick Examples — Click to Load

Calculation Mode

Input Values

%
pct_decrease
CALCULATED
$ calc --mode="findDecreased"
Decreased Value
80.00
Decrease Amount
20.00
Multiplier
0.8000
After 5 periods
32.77
Half-life: 3.11 periods
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Original vs Decreased

Depreciation Curve

Step-by-Step Breakdown

CALCULATION
Formula
Decreased = Original × (1 − p/100)
Multiplier
1 − 20/100 = 0.8000
1 - ext{percentage}/100
Decrease amount
100 × 0.2000 = 20.00
ext{Original} imes ext{percentage}/100
ANSWER
RESULT
80.00
After N periods
Value = 32.77
Original × (0.8000)^5
Half-life
3.11 periods
\text{ln}(0.5) / \text{ln}( ext{multiplier})

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

Key Takeaways

  • • Discount asymmetry: A 50% decrease followed by a 50% increase does not return you to the original value
  • • Depreciation: Assets lose value over time; successive decreases compound multiplicatively
  • • Half-life: The number of periods until a value reaches half its original when decreasing by a fixed % each period
  • • Multiplier: (1 − p/100) is the factor applied each period for a p% decrease
  • • 20% off then 20% off again is not 40% off total — it's 36% off (0.8 × 0.8 = 0.64)

Did You Know?

🏷️Retailers often use "50% off" rather than "half price" because percentage discounts feel more significant to consumersSource: Consumer Psychology
📉A 100% decrease means the value goes to zero — the item is completely gone or worthlessSource: Mathematics
🚗New cars typically lose 15–20% of value in the first year and ~10% per year after thatSource: Auto Industry
💱Currency devaluation of 5% means $1 buys 5% less — inflation is a form of percentage decrease in purchasing powerSource: Economics
⚖️Losing 2% body weight per week is often cited as a safe rate for sustainable weight lossSource: Health & Fitness
📊In half-life calculations, a 10% decrease per period has a half-life of ~6.6 periods (ln(0.5)/ln(0.9))Source: Exponential Decay

How It Works

Simple decrease: Value after decrease = Original × (1 − p/100). Example: 20% off $100 = $100 × 0.80 = $80.

Finding percentage: % Decrease = (Original − Decreased) / Original × 100. Example: $100 → $75 is (100−75)/100 × 100 = 25%.

Successive Decreases

If a value decreases by p% each period, after n periods: V_n = V_0 × (1 − p/100)^n. Two 20% decreases: 0.8 × 0.8 = 0.64, so 36% total decrease.

Expert Tips

Quick Mental Math

10% off: move decimal left. 25% off: take 1/4, subtract. 50% off: halve. 20% off: find 10%, double it, subtract.

Stacked Discounts

30% then 20% off = 0.70 × 0.80 = 0.56, so 44% total off — not 50%. Always multiply the remaining fractions.

Reverse the Decrease

If sale price is $80 after 20% off, original = $80 / 0.80 = $100. Divide by (1 − discount/100).

Half-Life Rule

For constant % decrease per period, half-life = ln(0.5) / ln(multiplier). Useful for depreciation and decay models.

Frequently Asked Questions

How do I calculate a value after a percentage decrease?

Multiply the original value by (1 − percentage/100). For example, 25% off $80 = $80 × 0.75 = $60.

How do I find the percentage decrease between two values?

Subtract the decreased value from the original, divide by the original, and multiply by 100. (Original − Decreased) / Original × 100.

Why don't two 50% decreases equal 100%?

Each decrease is applied to the new (smaller) value. 50% off $100 = $50. 50% off $50 = $25. Total decrease from $100 is 75%, not 100%.

What is half-life in percentage decrease?

The number of periods until the value reaches half of its original when it decreases by the same percentage each period.

How do successive percentage decreases work?

Multiply the value by (1 − p/100) for each period. After n periods: Value × (1 − p/100)^n.

Can I use this for discounts and depreciation?

Yes. Discounts are one-time decreases. Depreciation (cars, equipment) uses the same math applied repeatedly over time.

Quick Reference

×0.9
10% Decrease
×0.8
20% Decrease
×0.5
50% Decrease
ln(0.5)/ln(r)
Half-Life

Disclaimer: This calculator provides mathematical results for educational and practical purposes. For financial decisions (depreciation, investments), consult a qualified professional. Rounding may cause small differences in displayed values.

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