Mental Math: Percentage Tricks Everyone Should Know
Simple tricks for calculating percentages in your head - including the reversal trick, the 10% base method, and how to handle successive percentage changes.
Percentages come up constantly - tips, discounts, taxes, investment returns - and reaching for a calculator every time is slow. These mental math techniques let you calculate most percentages in seconds.
The Reversal Trick
This is the single most useful percentage trick:
X% of Y = Y% of X
This works because multiplication is commutative: (X/100) x Y = (Y/100) x X.
Examples:
- 8% of 25 = 25% of 8 = 2
- 4% of 75 = 75% of 4 = 3
- 6% of 50 = 50% of 6 = 3
- 15% of 40 = 40% of 15 = 6
- 3% of 200 = 200% of 3 = 6
- 72% of 50 = 50% of 72 = 36
Whenever one of the two numbers makes for an easy percentage, flip it. “8% of 25” is hard to compute mentally. “25% of 8” (which is just 8 divided by 4) is trivial.
The 10% Base Method
Most percentages can be built from 10%, which is always easy - just move the decimal point.
10% of any number = move the decimal one place left.
- 10% of $85 = $8.50
- 10% of $230 = $23.00
- 10% of $17.40 = $1.74
From 10%, derive everything:
| Percentage | How to Calculate | Example (on $85) |
|---|---|---|
| 1% | 10% / 10 | $0.85 |
| 5% | 10% / 2 | $4.25 |
| 10% | Move decimal left | $8.50 |
| 15% | 10% + 5% | $8.50 + $4.25 = $12.75 |
| 20% | 10% x 2 | $17.00 |
| 25% | 20% + 5% | $17.00 + $4.25 = $21.25 |
| 30% | 10% x 3 | $25.50 |
| 33% | 10% x 3 + 1% x 3 | $25.50 + $2.55 = $28.05 |
| 40% | 10% x 4 | $34.00 |
| 50% | Divide by 2 | $42.50 |
| 75% | 50% + 25% | $42.50 + $21.25 = $63.75 |
Tip calculation shortcut
For a 20% tip: Calculate 10% and double it.
- Bill: $73 → 10% = $7.30 → 20% = $14.60
For a 15% tip: Calculate 10%, then add half of that.
- Bill: $73 → 10% = $7.30 → half = $3.65 → 15% = $10.95
For an 18% tip: Calculate 20% and subtract 2%.
- Bill: $73 → 20% = $14.60 → 2% = $1.46 → 18% = $13.14
Percentage Increase and Decrease
Quick multipliers
Thinking in multipliers is faster than calculating the percentage and adding/subtracting:
| Change | Multiplier | Example |
|---|---|---|
| +5% | x 1.05 | $100 → $105 |
| +10% | x 1.10 | $100 → $110 |
| +15% | x 1.15 | $100 → $115 |
| +20% | x 1.20 | $100 → $120 |
| +25% | x 1.25 | $100 → $125 |
| +50% | x 1.50 | $100 → $150 |
| -10% | x 0.90 | $100 → $90 |
| -20% | x 0.80 | $100 → $80 |
| -25% | x 0.75 | $100 → $75 |
| -33% | x 0.67 | $100 → $67 |
| -50% | x 0.50 | $100 → $50 |
The discount shortcut
Instead of calculating the discount amount and subtracting, multiply by the complement:
- 30% off $60: Instead of calculating $18 and subtracting, just do 70% of $60 = $42. (60 x 0.7 = 42)
- 15% off $80: 85% of $80 = $68. (80 x 0.85 = 8 x 8.5 = 68)
Successive Percentage Changes
This is where most people’s intuition fails.
A 50% increase followed by a 50% decrease does NOT get you back to the start.
$100 → +50% → $150 → -50% → $75
You lost $25. Why? The 50% increase is calculated on $100, but the 50% decrease is calculated on $150 (a larger base). The decrease takes away more than the increase added.
The general formula:
Starting value x (1 + a) x (1 - b) = Final value
For equal opposite changes: $100 x (1 + 0.50) x (1 - 0.50) = $100 x 1.50 x 0.50 = $75
Successive increases:
Two consecutive 10% increases is NOT a 20% increase.
$100 x 1.10 x 1.10 = $100 x 1.21 = $121 (a 21% total increase)
The extra 1% comes from compounding - you’re earning 10% on the first 10% increase.
Three quick examples:
Stock drops 20% then gains 20%: $1,000 → $800 → $960. You’re still down $40 (4%).
Stock drops 50% - what gain is needed to recover? $1,000 → $500. To get back to $1,000, you need a 100% gain on $500.
Price goes up 25% then down 20%: $100 → $125 → $100. Back to the start! This is because (1 + 0.25) x (1 - 0.20) = 1.25 x 0.80 = 1.00.
The percentage recovery table
How much you need to gain to recover from a loss:
| Loss | Required Gain to Recover |
|---|---|
| -10% | +11.1% |
| -20% | +25% |
| -25% | +33.3% |
| -30% | +42.9% |
| -40% | +66.7% |
| -50% | +100% |
| -60% | +150% |
| -75% | +300% |
| -90% | +900% |
This is why avoiding large losses is so important in investing. A 50% drop requires a 100% gain just to break even.
Calculating Percentage Change
Percentage change = (New - Old) / Old x 100
Shortcut for common scenarios:
Price went from $80 to $100: Change = $20. What percentage of $80 is $20? $20/$80 = 1/4 = 25% increase
Revenue went from $150K to $120K: Change = -$30K. What percentage of $150K is $30K? $30K/$150K = 1/5 = 20% decrease
The fraction trick:
Convert the change to a fraction and simplify:
- Change of $15 on a base of $60: 15/60 = 1/4 = 25%
- Change of $12 on a base of $48: 12/48 = 1/4 = 25%
- Change of $7 on a base of $35: 7/35 = 1/5 = 20%
Percentage of a Percentage
What is 30% of 40%?
Multiply the decimals: 0.30 x 0.40 = 0.12 = 12%
If 60% of your customers are female and 25% of females buy product X, what percentage of all customers buy product X?
0.60 x 0.25 = 0.15 = 15%
Working Backwards from a Percentage
A sweater costs $68 after a 15% discount. What was the original price?
$68 = 85% of the original price (100% - 15% = 85%) Original = $68 / 0.85 = $80
You paid $9 in tax on a purchase. The tax rate is 6%. What was the pre-tax price?
$9 = 6% of the price Price = $9 / 0.06 = $150
General formula: Original = Final amount / (1 + or - percentage as decimal)
The “Roughly” Approach
For quick estimates, round aggressively:
- 18% of $43: Round to 18% of $40 = 20% of $40 - 2% of $40 = $8 - $0.80 = $7.20 (exact: $7.74)
- 7.5% tax on $29.99: Round to 7.5% of $30 = $2.25. Close enough for a quick check. (Exact: $2.25)
- 23% of $87: Round to 25% of $88 = $22. (Exact: $20.01 - the rounding was aggressive, so this is an overestimate, but it gives you the right ballpark.)
For everyday calculations (estimating tips, checking sale prices, approximating taxes), being within 5–10% of the exact answer is good enough. Save precision for when it matters.
Practice Makes Permanent
The best way to internalize these tricks is to practice them in real situations:
- Calculate the tip in your head before looking at the suggested amounts
- Estimate the sale price before looking at the tag
- Calculate percentage changes on stock prices or monthly expenses
- Check receipts for correct tax calculations
Within a few weeks of conscious practice, these calculations become automatic. The reversal trick alone will handle about 30% of the percentage problems you encounter.
Try the calculator: percentage calculator