Complete Percentage Calculator Guide 2026

"How much is 30% off this product?" "If it increased by 15% compared to last year, what's the actual amount?"

Percentages appear everywhere in daily life. But when it comes to calculating them, many people get confused. This guide covers everything you need to know about percentage calculations.

---

What is a Percentage?

Percentage (%) means "per hundred".

Percentage = (Part / Whole) × 100

Basic Concepts

Percentage ↔ Decimal Conversion

Percentage → Decimal: Divide by 100
  25% → 25 ÷ 100 = 0.25

Decimal → Percentage: Multiply by 100
  0.75 → 0.75 × 100 = 75%

---

Core Percentage Calculation Types

1. What is X% of the Total?

Formula: Total × (Percentage / 100)

Problem: What is 20% of $500?
Solution: 500 × (20 / 100) = 500 × 0.2 = $100

Real-life examples:

• Saving 10% of a $3,000 salary = $300
• 15% of 100 people attending = 15 people

2. A is What Percentage of B?

Formula: (A / B) × 100

Problem: 30 is what percentage of 120?
Solution: (30 / 120) × 100 = 25%

Real-life examples:

• 80/100 points = 80%
• Net profit of $40,000 out of $200,000 revenue = 20%

3. If X% equals A, What is the Total?

Formula: A / (Percentage / 100)

Problem: If 20% is $50, what is the total?
Solution: 50 / 0.2 = $250

---

Discount Calculations

Calculating Discount Amount

Discount Amount = Original Price × (Discount Rate / 100)
Final Price = Original Price - Discount Amount
            = Original Price × (1 - Discount Rate/100)

Example: 30% off a $100 product

Discount Amount: 100 × 0.3 = $30
Final Price: 100 - 30 = $70

Or
Final Price: 100 × 0.7 = $70

Reverse Discount Calculation

Finding the original discount rate from the discounted price:

Discount Rate = ((Original Price - Sale Price) / Original Price) × 100

Example: Original $80 → Sale price $60

Discount Rate = ((80 - 60) / 80) × 100
             = (20 / 80) × 100
             = 25%

Stacked Discounts Warning

30% off plus an additional 20% off is NOT 50% off!

Original Price: $100
After 30% off: 100 × 0.7 = $70
Additional 20% off: 70 × 0.8 = $56

Actual total discount: (100 - 56) / 100 × 100 = 44%

---

Percentage Change Calculations

Increase Rate

Increase Rate = ((New Value - Previous Value) / Previous Value) × 100

Example: Revenue from $100M to $120M

Increase Rate = ((120M - 100M) / 100M) × 100 = 20%

Decrease Rate

Decrease Rate = ((Previous Value - New Value) / Previous Value) × 100

Example: Costs from $5M to $4M

Decrease Rate = ((5M - 4M) / 5M) × 100 = 20%

Calculating Value After Change

After X% increase: Original Value × (1 + X/100)
After X% decrease: Original Value × (1 - X/100)

Examples:

• 100 → 25% increase → 100 × 1.25 = 125
• 100 → 25% decrease → 100 × 0.75 = 75

Trap: Increase Then Decrease

If 100 increases by 50% then decreases by 50%, does it return to original?

100 × 1.5 = 150 (50% increase)
150 × 0.5 = 75 (50% decrease)

Result: 75 (NOT the original 100!)

---

Margin Calculations

Margin vs Markup

Margin Calculation

Margin = ((Selling Price - Cost) / Selling Price) × 100

Example: Cost $70, Selling Price $100

Margin = ((100 - 70) / 100) × 100 = 30%

Markup Calculation

Markup = ((Selling Price - Cost) / Cost) × 100

Example: Cost $70, Selling Price $100

Markup = ((100 - 70) / 70) × 100 ≈ 42.86%

Margin → Markup Conversion

Markup = Margin / (1 - Margin/100)

Example: 30% Margin

Markup = 30 / (1 - 0.3) = 30 / 0.7 ≈ 42.86%

---

Real-life Percentage Examples

1. Sale Shopping

Situation: A $89 item at 35% off + additional 10% coupon

35% off: 89 × 0.65 = $57.85
10% additional: 57.85 × 0.90 = $52.07

Total discount rate: (89 - 52.07) / 89 × 100 ≈ 41.5%

2. Tip Calculation

Situation: Meal cost $45, 15% tip

Tip amount: 45 × 0.15 = $6.75
Total: 45 + 6.75 = $51.75

3. Grade Calculation

Situation: Midterm 40/50, Final 75/100, weighted 40:60

Midterm converted: (40/50) × 40 = 32 points
Final converted: (75/100) × 60 = 45 points
Total: 32 + 45 = 77 points

4. Salary Taxes

Situation: $50,000 annual salary, effective tax rate calculation

Income tax: ~$4,500 (9%)
Social Security: ~$3,100 (6.2%)
Medicare: ~$725 (1.45%)
...

Net pay: ~$41,000
Effective deduction rate: (9,000 / 50,000) × 100 = 18%

---

Quick Calculation Tips

Mental Math Tricks

Example: 15% of $780

10% = $78
5% = $39 (78 ÷ 2)
15% = 78 + 39 = $117

---

Common Mistakes

1. Percentage Points vs Percentage

Interest rate 2% → 3%

❌ "50% increase" (common misstatement)
✅ "1 percentage point increase" or "50% increase"

1 percentage point = absolute change (2% → 3%)
50% = relative change ((3-2)/2 × 100)

2. Reference Value Confusion

A is 25% larger than B
vs
B is 25% smaller than A?

A = 125, B = 100
A is 25% larger than B: (125-100)/100 = 25% ✓
B is 20% smaller than A: (125-100)/125 = 20% ✓

Different references mean different percentages!

3. Compound Change Calculations

10% growth each year for 3 years

❌ Total 30% growth
✅ 100 × 1.1³ = 133.1 → 33.1% growth

---

FAQ

Q1: What's the difference between discount rate and margin?

A:

• Discount rate: How much is reduced from the original price (customer perspective)
• Margin: Profit ratio of the selling price (business perspective)

Q2: When should I round percentage decimals?

A:

• Finance: Usually 2 decimal places
• Statistics: 1-3 decimal places depending on context
• Daily use: Whole numbers

Q3: Can percentages exceed 100%?

A: Yes! 200% means 2 times, 150% means 1.5 times.

Last year's revenue: $100M
This year's revenue: $250M
Growth rate: ((250-100)/100) × 100 = 150%

Q4: What about percentage change from zero?

A: The increase rate from 0 to another value is undefined (cannot divide by 0)

---

Conclusion

Key percentage calculation summary:

1. Basic: Percentage = (Part / Whole) × 100
2. Discount: Final Price = Original × (1 - Discount Rate/100)
3. Change: Change Rate = (New - Previous) / Previous × 100
4. Margin: Margin = Profit / Selling Price × 100
5. Caution: Stacked discounts, distinguish percentage points

---

Related Tools