How to Subtract a Percentage
Shortcut: multiply by (1 minus the decimal). Subtracting 30% means multiplying by 0.70. Subtracting 15% means multiplying by 0.85. One step. This guide shows the two-step method too, gives five worked examples, covers VAT removal, and explains the asymmetry that catches people out.
The Two-Step Method
The long way to subtract a percentage from a number:
- Calculate the amount to subtract: Number x Percentage / 100.
- Subtract that from the original: Original minus the Amount.
Subtracting 30% from 250:
Step 1: 250 x 30 / 100 = 75.
Step 2: 250 minus 75 = 175.
Answer: 175.
The One-Step Shortcut
Subtract the percentage from 100 to get the "complement," convert to a decimal, and multiply:
New Value = Original x (1 minus Percentage / 100)
Subtracting 30%: 1 minus 0.30 = 0.70. Then 250 x 0.70 = 175. Same answer, one step.
Subtracting 15%: multiply by 0.85.
Subtracting 7%: multiply by 0.93.
Subtracting 50%: multiply by 0.50 (same as halving).
Multiplier Quick Reference
| Subtract This % | Multiply By | Example on $500 |
|---|---|---|
| 5% | 0.95 | $475 |
| 10% | 0.90 | $450 |
| 15% | 0.85 | $425 |
| 20% | 0.80 | $400 |
| 25% | 0.75 | $375 |
| 40% | 0.60 | $300 |
| 50% | 0.50 | $250 |
Worked Examples
Sale price with 35% off
Original price: $180. Discount: 35%.
180 x 0.65 = $117. You save $63.
Salary cut of 8%
Current salary: $62,000. Reduction: 8%.
62,000 x 0.92 = $57,040. The cut is $4,960.
Calories removed from recipe
Original recipe: 650 calories. You cut fat, reducing calories by 22%.
650 x 0.78 = 507 calories.
Budget cut
Marketing budget: $24,000. Company cuts it 12.5%.
24,000 x 0.875 = $21,000. (12.5% as a decimal is 0.125; 1 minus 0.125 = 0.875.)
Commission deducted
You sell a house for $320,000 and the agent charges 2.5%.
320,000 x 0.975 = $312,000. Agent's fee: $8,000.
Removing VAT or Tax Already Included in a Price
When a price already includes VAT and you need the pre-tax amount, do not subtract the percentage directly. Divide by the multiplier instead:
Pre-tax Price = Total Price / (1 + Tax Rate / 100)
A $120 item includes 20% VAT. Pre-tax: 120 / 1.20 = $100. (Subtracting 20% of $120 would give $96, which is wrong.)
Why? Because the tax was added to the pre-tax price, not the final price. The $120 is 120% of the original $100, not 100% of something plus 20% of $120.
The Asymmetry Trap
Subtracting a percentage and then adding the same percentage back does not return you to the start. Subtract 20% from 100: 100 x 0.80 = 80. Add 20% to 80: 80 x 1.20 = 96. You end up at 96, not 100.
The reason: the second operation is calculated on the smaller number (80), not the original (100). To undo a 20% subtraction, you need to add back more than 20%. Specifically: 80 / 0.80 = 100. You need a 25% addition to reverse a 20% subtraction.
This connects to the broader discussion in percentage decrease. The companion article, how to add a percentage to a number, covers the reverse operation in full.
Using the Calculator
The percentage calculator can handle subtraction through the percent change section or by using the "X% of Y" section to find the discount amount, then doing a simple subtraction. Either path gets you there quickly.
Frequently Asked Questions
How do I subtract a percentage from a number?
Multiply the number by (1 minus the percentage as a decimal). To subtract 25% from 200: 200 x 0.75 = 150.
How do I remove VAT from a price?
Divide the VAT-inclusive price by (1 plus the VAT rate as a decimal). At 20% VAT: price / 1.20.
If I subtract 20% then add 20%, do I get back to the start?
No. Subtract 20% from 100 to get 80. Add 20% of 80 (which is 16) to get 96, not 100. The two operations are on different bases.
What is 15% off $120?
120 x 0.85 = $102. The discount amount is $18.