Percentages and aspect ratios look like two different subjects, but they cause the same kind of mistake: a calculation that feels right and is quietly wrong. A 50% drop followed by a 50% rise does not get you back to where you started. Two discounts of 20% and 10% do not make 30%. Cropping a photo to a wider shape does not lose “a little”. We worked through the most common cases and wrote down the real numbers, including the ones people most often get wrong when pricing, reading a bill or sizing a picture.
Percent changes do not cancel each other out
A percentage is always a share of the current number. After a drop the base is smaller, so the same percentage rise adds less than the drop took away. To get back to even, the rise has to be larger than the fall:
| If it falls by | It must rise by |
|---|---|
| 10% | 11.1% |
| 20% | 25% |
| 30% | 42.9% |
| 40% | 66.7% |
| 50% | 100% |
| 75% | 300% |
The formula is rise needed = 1 ÷ (1 − fall) − 1. The reverse order does not rescue you either. A price that goes up 20% and then down 20% ends 4% lower (1.20 × 0.80 = 0.96), up 25% then down 25% ends 6.3% lower, and up 50% then down 50% ends 25% lower. This is why a fund that loses 50% needs to double just to break even.
Stacked discounts multiply
A shop offers “20% off, plus an extra 10% at checkout”. The second discount applies to the already reduced price, so you pay 0.80 × 0.90 = 72% of the original, a saving of 28%.
| Discounts | What adding them suggests | What you actually save |
|---|---|---|
| 20% then 10% | 30% | 28% |
| 30% then 20% | 50% | 44% |
| 50% then 20% | 70% | 60% |
| 40% then 40% | 80% | 64% |
| 25% three times | 75% | 57.8% |
The gap grows with the size of the discounts. “Up to 80% off” made of two 40% steps is really 64% off. The Percentage Calculator has a Discount & Tax mode for chains like this.
Margin and markup are not the same
Markup is profit as a share of the cost. Margin is profit as a share of the selling price. A product that costs ₹100:
| Markup on cost | Selling price | Margin on price |
|---|---|---|
| 10% | ₹110 | 9.1% |
| 20% | ₹120 | 16.7% |
| 25% | ₹125 | 20% |
| 30% | ₹130 | 23.1% |
| 50% | ₹150 | 33.3% |
| 100% | ₹200 | 50% |
A margin is always smaller than the matching markup, and the difference grows as the numbers rise. If you want a particular margin, the markup you need is margin ÷ (1 − margin): a 20% margin needs a 25% markup, a 30% margin needs 42.9%, a 40% margin needs 66.7% and a 50% margin needs a 100% markup. Mixing the two up is one of the most common pricing errors, because you under-price by exactly this gap.
Taking GST or VAT out of a total
When a price already includes tax, the tax is a share of the pre-tax price, not of the total. So you divide by (1 + rate). Multiplying by (1 − rate) is a common shortcut and it is wrong. For a ₹1,180 total:
| Tax rate | Correct price before tax | Tax inside the total | Shortcut (total × (1 − rate)) | Shortcut is off by |
|---|---|---|---|---|
| 5% | ₹1,123.81 | ₹56.19 | ₹1,121.00 | ₹2.81 |
| 18% | ₹1,000.00 | ₹180.00 | ₹967.60 | ₹32.40 |
| 40% | ₹842.86 | ₹337.14 | ₹708.00 | ₹134.86 |
The error grows with the rate. At 5% it is small, which is why the shortcut survives, and at 18% or 40% it becomes a real amount on every invoice. To add tax, multiply by (1 + rate). To remove it, divide. The GST Calculator does both and splits the result into CGST, SGST or IGST.
Percentage points are not percent
If an interest rate moves from 4% to 5%, it rose by 1 percentage point but by 25 percent (1 ÷ 4). Both statements are true, and headlines use whichever sounds bigger. When you read “rose by 25%”, check what the base was. The same goes for the three questions that sound alike: 20 is 25% of 80, 20 is 25% more than 16, and 16 is 20% less than 20. Each is a different calculation.
Resizing without squashing the picture
An aspect ratio is width ÷ height. To resize without distortion, change one side and let the other follow: new height = new width × (original height ÷ original width). A 4000 × 3000 photo (4:3) resized to 1600 wide should be 1200 tall. If you set both sides yourself and the ratio differs, the picture is stretched.
Whole-number heights are where it gets fiddly. At 16:9 a width gives a whole-number height only when it is a multiple of 16 (1280 → 720, 1920 → 1080, 3840 → 2160). A 1000 px wide image would need 562.5 px, and 1366 wide needs 768.38, which is why the old 1366 × 768 screen size is off true 16:9 by 0.05%. The matching steps are 4 for 4:3, 3 for 3:2 and 4 for 4:5 (1080 wide → 1350 tall, the Instagram portrait size). When you need exact sizes, pick a width from those steps and the height will be a clean integer.
What you lose when you crop to a different shape
Changing the shape without stretching means cropping, and that removes pixels. This table shows the share of the original picture that survives a centred crop:
| Starting shape | To 16:9 | To 1:1 | To 4:5 | To 9:16 |
|---|---|---|---|---|
| 4:3 (many phones, compact cameras) | 75% | 75% | 60% | 42% |
| 3:2 (DSLR and mirrorless) | 84% | 67% | 53% | 38% |
| 16:9 (video) | 100% | 56% | 45% | 32% |
So turning a 16:9 video frame into a vertical 9:16 clip keeps under a third of the frame. That is why subjects have to be framed in the middle if the same footage will be posted in more than one shape. Leave room around the subject if you plan to crop. Our guides to social media image sizes and video resolution and aspect ratio show the sizes each platform uses.
Doing it quickly
- For percentages, open the Percentage Calculator and choose the mode that matches your question: P% of X, X is what % of Y, increase or decrease, reverse %, or Discount & Tax.
- For shapes, open the Aspect Ratio Calculator, enter the width and height, and use the presets for YouTube, Reels, Instagram square and portrait, or a monitor.
- Resize the file to the exact size with the Image Resizer, keeping the ratio locked.
The calculators run in your browser, so nothing you enter is uploaded. The figures here are exact arithmetic, but they show maths only. They do not account for rounding rules on a particular invoice or for taxes that apply differently in your country.
