How to Add a Percentage to a Number
Shortcut: multiply by (1 plus the decimal). To add 20% to a number, multiply by 1.20. To add 7.5%, multiply by 1.075. One step instead of two. This guide shows the two-step method, the shortcut, and how they both produce the same answer.
The Two-Step Method
The long way to add a percentage:
- Calculate the percentage of the number: Number x Percentage / 100.
- Add that amount to the original number.
Example: add 25% to 160.
Step 1: 160 x 25 / 100 = 40.
Step 2: 160 + 40 = 200.
Answer: 200. This works every time and is straightforward to follow.
The One-Step Shortcut
The faster approach: convert the percentage to a multiplier and apply it in a single step.
New Value = Original x (1 + Percentage / 100)
Adding 25% becomes multiplying by 1.25: 160 x 1.25 = 200. Same answer, half the keystrokes.
The logic: the "1" preserves the original, and the decimal fraction adds the increase on top of it.
Multiplier Quick Reference
| Add This % | Multiply By | Example on $400 |
|---|---|---|
| 5% | 1.05 | $420 |
| 10% | 1.10 | $440 |
| 15% | 1.15 | $460 |
| 20% | 1.20 | $480 |
| 25% | 1.25 | $500 |
| 50% | 1.50 | $600 |
| 7.5% | 1.075 | $430 |
| 12.5% | 1.125 | $450 |
Real-World Examples
Tips at a restaurant
Bill: $64. You want to leave 18%.
One step: 64 x 1.18 = $75.52. The tip itself is $11.52.
Two steps: 64 x 0.18 = 11.52. Then 64 + 11.52 = $75.52. Same thing.
Adding VAT (20%)
A product costs $85 before tax. With 20% VAT:
85 x 1.20 = $102. The tax itself is $17.
Salary increase
Current salary: $52,000. You get a 6% raise.
52,000 x 1.06 = $55,120. The raise in dollar terms: $3,120.
Price increase after inflation
A service cost $280 last year. Costs rose 8%.
280 x 1.08 = $302.40.
Investment return
Portfolio: $10,000. Return this year: 11%.
10,000 x 1.11 = $11,100. Gain: $1,100.
Is Adding 10% Twice the Same as Adding 20%?
No, and the gap matters in compound growth. Adding 10% once: 1,000 x 1.10 = 1,100. Adding 10% again: 1,100 x 1.10 = 1,210. Total increase: 21%. Adding 20% once: 1,000 x 1.20 = 1,200. Total increase: 20%.
Two steps of 10% produce 1% more than one step of 20%, because the second increase is applied to an already-larger base. The extra 1% comes from the compounding. Small gap here, but it builds over many periods into the difference between savings accounts that look similar on paper.
Reversing an Addition: Finding the Original
If you know the final number and the percentage that was added, divide by the multiplier:
Original = Final / (1 + Percentage / 100)
A price of $138 already includes a 15% markup. Original: 138 / 1.15 = $120.
A salary of $53,040 includes a 4% raise. Previous salary: 53,040 / 1.04 = $51,000.
Connection to Subtraction
Adding a percentage and subtracting a percentage are mirror operations. Adding 20% multiplies by 1.20; subtracting 20% multiplies by 0.80. They do not cancel each other out: add 20% to 100 to get 120, then subtract 20% of 120 (24) to get 96, not 100. See how to subtract a percentage for the full explanation and percentage increase for the companion calculation.
Frequently Asked Questions
How do I add a percentage to a number?
Multiply the number by (1 plus the percentage as a decimal). To add 20% to 150: 150 x 1.20 = 180.
What is 15% added to $80?
80 x 1.15 = $92. Or: 15% of 80 is 12, and 80 + 12 = $92.
How do I add VAT to a price?
Multiply the pre-tax price by (1 plus the VAT rate as a decimal). At 20% VAT: price x 1.20. At 10% VAT: price x 1.10.
Is adding 10% twice the same as adding 20% once?
No. Adding 10% twice gives 121% of the original, a 21% total increase. Adding 20% once gives 120%. The two-step version is slightly larger due to compounding.