Ratio Calculator

Related Calculators

Ratio: A comparison of two numbers written like A:B.

Simplified ratio: The ratio written in lowest whole-number terms, such as 6:8 becoming 3:4.

Ratio as fraction A/B: The same ratio written as a fraction, using the first term on top and the second term on the bottom.

Ratio as decimal: The value you get from A divided by B, if B is not 0.

Equivalent ratios: Ratios that describe the same relationship, such as 2:3 and 10:15.

Proportion: An equation that says two ratios are equal, like A:B = C:D [1].

Scale factor: The number used to multiply both parts of a ratio to make an equivalent ratio.

Percent of total: The share of the total A+B that comes from one term, written as a percent.

Mistake: Leaving "Second term B" blank and expecting the calculator to treat it as 0.
Fix: Enter a real number in "Second term B". Blank required fields cause an error instead of being guessed.

Mistake: Typing 0 for both "First term A" and "Second term B" and expecting a valid "Simplified ratio".
Fix: Change at least one of those values. A ratio of 0:0 is undefined, so the calculator will show "Warning or undefined case".

Mistake: In solve mode, filling all four ratio values and also choosing "Missing value to solve".
Fix: Leave exactly one of "First term A," "Second term B," "First term C," or "Second term D" empty so the calculator can find the "Solved missing value".

Mistake: Comparing ratios with "Second term B" or "Second term D" equal to 0, then expecting a normal "Ratio as decimal" result.
Fix: The ratio can still be shown, but "Ratio as decimal" is undefined when the second term is 0. Check "Equivalent?" and "Warning or undefined case" instead.

Mistake: Entering decimals like 1.5 and 2.25, then thinking the calculator rounded them before making "Simplified ratio".
Fix: It first clears decimals exactly, then reduces the ratio. Read the steps and compare with "Ratio as fraction A/B" if you want to verify.

Mistake: Using different units inside the same ratio, like inches for "First term A" and feet for "Second term B".
Fix: Convert both terms to the same unit before using "Simplified ratio," "Equivalent?," or "Equivalent ratios list".

• The calculator treats a ratio as undefined when both terms are zero, so 0:0 will not simplify.
• "Ratio as decimal" and "Ratio as fraction A/B" are undefined when the second term of the current ratio is 0.
• "A as percent of total" and "B as percent of total" are undefined when A+B=0 because the total is zero.
• In compare mode, a result can only be tested when both ratios are mathematically defined enough for cross-products or exact normalized forms.
• In solve mode, exactly one value must be missing, and the needed denominator in the formula cannot be 0.
• Decimal normalization is exact for terminating decimals entered in the boxes. Very long decimal entries may display rounded final decimals even when the internal ratio logic is exact enough to simplify.
• The calculator does not convert units for you. If your two terms use different units, convert them first or the ratio may be misleading.
• Negative ratios are allowed, but their meaning depends on context. In many real-life part-to-whole situations, negative terms do not make sense even though the arithmetic works.

How the calculator works

The calculator uses one current ratio A:B for simplification, fraction form, decimal form, and percent-of-total outputs. In compare mode it also uses C:D. In solve mode it finds the one missing term that makes A:

B = C:D true [1][3].

Simplifying a ratio

g = gcd(|A|, |B|)

simplified ratio = (A/g) : (B/g)

For whole numbers, it finds the greatest common divisor and divides both terms by it. If one term is negative, the sign stays in the simplified result instead of being forced positive.

Clearing decimals exactly first

m = max(decimal places in A, decimal places in B)

k = 10^m

A' = A x k, B' = B x k

simplify A':B' with gcd

This is the key upgrade on the page. For a terminating decimal ratio like 1.5:2.25, the calculator first turns it into 150:225, then reduces it to 2:3. That avoids the common mistake of rounding first.

Fraction, decimal, and percent outputs

ratio as fraction = A/B

ratio as decimal = A/B

A as percent of total = 100 x A / (A+B)

B as percent of total = 100 x B / (A+B)

These outputs help you interpret the ratio. A larger decimal means the first term is larger compared with the second term. The two percent-of-total values add to 100% when the total is not zero.

Checking whether two ratios are equivalent

A:B and C:D are equivalent if A x D = B x C

The calculator uses the cross-product test for equivalence [1][1]. When possible, it also interprets the matching scale factor between ratios so you can see how one ratio was stretched from the other.

Solving one missing value in a proportion

D = (B x C) / A

C = (A x D) / B

B = (A x D) / C

A = (B x C) / D

If exactly one value is missing, the calculator rearranges the proportion and solves for that term. It blocks cases that would divide by zero.

Generating equivalent ratios

equivalent_n = (A_s x n) : (B_s x n), for n = 1, 2, ..., N

The list is based on the simplified ratio A_s:B_s so the pattern is easier to read. For example, if 4:10 simplifies to 2:

5 and N=4, the list is 2:5, 4:10, 6:15, 8:20.

Mini example

Suppose you enter A=6 and B=8 in simplify mode. The gcd of 6 and 8 is 2, so the simplified ratio is 3:

4. The decimal is 6/8 = 0.75. The total is 14, so A as percent of total is about 42.86% and B as percent of total is about 57.14%.

What can make real answers differ

This calculator follows exact arithmetic rules for ratios and proportions, but interpretation still matters. Mixed units, undefined zero cases, and negative values can make a mathematically correct result less useful in a real-life setting, so check that your inputs describe the same kind of quantity before trusting the result.