Ratio Calculator — proportions, simplifying, scaling, aspect ratios and fair shares
Ratio & Proportion Calculator
Six cards for everything ratios do: solve a proportion with any one term
missing, simplify messy ratios (decimals included), scale a recipe to a
new number of servings, aspect ratios for any screen or image, divide an
amount into shares like 2:3, and equivalent ratios for tables of values.
Every card works as you type. For percentage questions see the
Percentage Calculator; for general math the
Scientific Calculator.
1. Solve the proportion A : B = C : D — leave exactly one box empty
:
=
:
→
3 : 4 = 6 : ? → cross-multiply: 3 × D = 4 × 6, so D = 8.
2. Simplify a ratio (integers, decimals, two or three terms)
→
Separate terms with colons (or / or spaces). 0.5:1.5 → 1:3; 100:50:150 → 2:1:3.
3. Scale a recipe — one line per ingredient: amount name
recipe is for
servings → I need
Every amount is multiplied by 6 ÷ 4 = 1.5. Lines without a leading number are kept as-is.
4. Aspect ratio — from pixels, or find the missing side
width
× height
→
Missing side: ratio
known
=
→
1920×1080 is exactly 16:9. The match list covers 21:9, 16:10, 16:9, 3:2, 4:3, 5:4, 1:1, 9:16 and the golden ratio.
5. Divide an amount into a ratio (fair shares)
divide
in the ratio
→
100 split 2:3 → 40 and 60: each part is total × share ÷ sum-of-shares.
6. Equivalent ratios — the multiplication table of a ratio
× how many rows
3:4, 6:8, 9:12 … all describe the same relationship — that is what "equivalent" means.
Try an example:
Cross-multiplication in one line: A : B = C : D is true exactly when
A × D = B × C — the diagonal products are equal. Solving any
proportion is therefore just "multiply the two knowns on one diagonal, divide by the
remaining known". Privacy: everything runs in this tab.
What is a ratio?
A ratio compares two quantities by division, not by subtraction. "3 : 4" does not
mean "one more" — it means the first quantity is 3/4 = 75% of the second, whatever
their sizes. That single idea powers map scales (1 : 25000), recipes, gear trains, screen
shapes, mixing paint and splitting bills: anywhere the relationship must survive
while the amounts change.
Question
Ratio view
Answer
Map: 1 cm to 25,000 cm
1 : 25000
4 cm on paper = 1 km on the ground
Recipe: 2 cups flour, 1 tsp salt
2 : 1
triple the recipe → 6 cups, 3 tsp — ratio unchanged
Screen: 1920 × 1080 pixels
1920 : 1080 = 16 : 9
any other 16:9 screen shows the same shape
Why cross-multiplication works
A : B = C : D says A/B = C/D. Multiply both sides by B and by D and the denominators
cancel, leaving A × D = B × C — the two diagonal products of the
proportion. To find a missing term, cover it up and compute
(product of the diagonal across from it) ÷ (the remaining term). For 3 : 4 = 6 : ?,
the diagonal across from ? is 3 × 4 = 12, and the remaining term is 6, so ? = 12 ÷ 6 = 2…
careful — the rule is: D = (B × C) / A = (4 × 6) / 3 = 8. Always keep the
letters straight; the card above does it for you.
Simplifying, including decimals
Divide every term by the same number and the ratio is unchanged. 8 : 12 → both
divisible by 4 → 2 : 3. For decimals, first scale up to whole numbers: 0.5 : 1.5
→ ×10 → 5 : 15 → ÷5 → 1 : 3. A three-term ratio like
100 : 50 : 150 simplifies with the gcd of all three (here 50) to 2 : 1 : 3.
The aspect-ratio zoo
Ratio
Typical use
1920-wide example
21 : 9
ultrawide monitors
1920 × ~823
16 : 9
HD TV, most monitors
1920 × 1080
16 : 10
older laptops
1920 × 1200
3 : 2
35 mm photos, many phones
1920 × 1280
4 : 3
classic TV, iPads
1920 × 1440
1 : 1
square
1920 × 1920
φ ≈ 1.618 : 1
golden rectangle
1920 × ~1186
The golden ratio 1.618… is the one famous ratio that cannot be written as a
ratio of whole numbers — it is irrational — so 1000 × 618 only
approximates it.
FAQ
Ratio vs fraction? — a fraction is one number (3/4); a ratio can compare three
or more things at once (2:3:5), which no single fraction can. Can ratio terms be zero? — a zero term is allowed in a comparison (0 : 5) but
makes solving proportions impossible when it sits where you must divide; the cards flag it. Why is my aspect ratio not exactly 16:9? — some panels are 1366 × 768
(683 : 384 ≈ 16 : 8.99), off by a rounding choice in hardware; the card shows the exact
simplified form plus the nearest common match. Dividing with remainders? — money split 100 in 3 : 3 : 4 gives 30, 30, 40 —
exact; but 100 in 1 : 1 : 1 gives 33.33… each; the card shows rounded values and the
exact fractions so nothing hides. Does anything leave my machine? — no: no server, no storage, no analytics.
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