Ratio Calculator
Four modes: simplify a ratio to lowest terms, scale a ratio by a factor, solve proportions for a missing value (a:b = c:?), and split a total amount into ratio parts.
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How It Works
Enter two numbers a and b. The calculator divides both by GCF(a,b) using the Euclidean algorithm. Result shows: simplified ratio, decimal value (a/b), and percentage. For 60:100: GCF=20, simplified=3:5=0.6=60%. Also shown: the original ratio for confirmation and the GCF used.
Simplified a:b = (a/GCF):(b/GCF)60:100 → simplified 3:5, decimal 0.6, percent 60%Enter ratio a:b and the scale factor. Scaled ratio = (a×factor):(b×factor). Scale factor can be any positive number including decimals. Scale 3:4 by 2.5 → 7.5:10. Scale 1:50000 (map) by 0.00005 to get real distances. Negative scale factors are not accepted — use positive values only.
Scaled = (a×k):(b×k) for any positive k3:4 × 2.5 → 7.5:10 | 1:100 × 5 → 5:500Enter three of the four values in a:b = c:d. Leave one field blank — the calculator solves for it via cross-multiplication: d = b×c/a (or any other rearrangement). Example: 3:4 = ?:12 → ? = 3×12/4 = 9. The equation display shows which proportion was solved.
Cross-mult: a×d = b×c → solve for unknown3:4 = ?:12 → ?=9 | 5:? = 15:24 → ?=8Enter the ratio parts (up to three parts, e.g. 2:3:1) and the total amount. Each share = (part/total_parts) × total. For $900 split 2:3:1: total_parts=6, shares = $300, $450, $150. Verify: 300+450+150=900 ✓. Works for any unit: money, area, time, materials.
Share_i = (part_i / Σparts) × total2:3:1 split of $900 → $300, $450, $150A ratio 2:3 means "2 parts A for every 3 parts B." The fraction of the total that is A: 2/(2+3) = 2/5 = 40%. The fraction that is B: 3/5 = 60%. So in a class with 2:3 ratio of boys to girls, girls are 3/5 = 60% of the class — NOT 3/2 = 150%. Simplify mode shows the decimal form a/b as the ratio value, not the fraction of total.
Ratio a:b → fraction A = a/(a+b) B = b/(a+b)Ratio 2:3 → A is 2/5=40% of total, B is 3/5=60%Quick Reference
Verify these in the calculator above.
Simplify
12:18 simplified
2:3
Simplify
Decimal of 3:4
0.75
Scale
3:4 × 2.5
7.5:10
Proportion
3:4 = ?:12
"?"=9
Proportion
5:8 = 15:?
"?"=24
Split
Split $600 in 1:2:3
$100,$200,$300
Scale
Map 1:50000, 2cm
1 km real
Fraction
Ratio 2:3 → % A
40%
Tips & Shortcuts
Simplify mode shows the decimal form (a÷b) alongside the ratio — useful for comparing two ratios: the one with the higher decimal value is the larger ratio.
For recipe scaling: enter original ratio in Simplify mode to see the base ratio, then use Scale mode with your multiplier to get new quantities.
Proportion mode solves for any of the four values — just leave one blank. The equation display confirms which proportion was solved.
In Split Total mode, the ratio parts do not need to sum to any specific number — enter the raw parts (2,3,1) and any total amount.
To check if two ratios are equivalent: simplify both and compare. If they simplify to the same a:b, they are equivalent.
Common Mistakes
Thinking ratio 2:3 means 2/3 of the total
Ratio 2:3 means 2 parts out of a total of 5 parts (2+3). The fraction of total that is part A = 2/5 = 40%, not 2/3. Use Split Total mode to see each part as a fraction of the whole.
Leaving both fields blank in Proportion mode
Proportion mode needs exactly three known values and one blank. Leaving two blank makes the problem under-determined — infinitely many solutions exist.
Using negative scale factors in Scale mode
Scale factors must be positive — ratios represent magnitudes. For a reciprocal relationship (ratio 3:4 → 4:3), swap the values before scaling rather than using a negative factor.
Simplifying fractions vs ratios differently
Simplifying 12:18 and 12/18 both divide by GCF=6, giving 2:3 and 2/3. The processes are identical. The difference is interpretation: 2:3 is a ratio between two quantities; 2/3 is a fraction of a whole.
Forgetting to add parts in Split Total
The total parts denominator is the SUM of all ratio values (2+3+1=6), not the largest part. Each share = part/sum × total, not part/max × total.
Frequently Asked Questions
Divide both parts by their GCF. For 12:18: GCF=6, simplified = 2:3. Enter 12 and 18 in Simplify mode. The decimal form (12/18 = 0.667) and percentage also display.
Cross-multiply. For a:b = c:d, missing d = b×c/a. Enter a=3, b=4, c=9 in Proportion mode → d=12. Check: 3/4 = 9/12 = 0.75 ✓.
Multiply both parts by the scale factor. Ratio 3:4 scaled by 2.5 → 7.5:10. Enter 3, 4, and scale factor 2.5 in Scale mode.
In Split Total mode, enter the ratio parts and the total. Example: split $600 in ratio 2:3:1. Total parts=6. Each share: 2/6×600=$200, 3/6×600=$300, 1/6×600=$100. Verify: 200+300+100=600 ✓.
Two ratios are equivalent if they simplify to the same ratio. 4:6 and 8:12 are both equivalent to 2:3. Use Proportion mode or Simplify mode to check: if both simplify to the same result, they are equivalent.
A ratio a:b represents a relationship between two quantities. A fraction a/b represents a portion of a whole. 3:4 means "3 for every 4." The fraction 3/4 means "3 out of 4." Ratio 2:3 does NOT mean 2/3 of the total — it means 2 parts out of a 2+3=5 part total, so 2/5 of the whole.
Cross-multiply: if a/b = c/d, then a×d = b×c, so d = b×c/a. Example: 5/8 = 15/x → x = 8×15/5 = 24. Verify: 5/8 = 15/24 = 0.625 ✓. Enter any three values in Proportion mode.
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