Ratio Calculator: Simplify Ratios, Solve Proportions, Share in a Ratio and Compare Unit Prices
Ratios and proportions with the steps.
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Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.
How this calculator works
Choose simplify, solve, share or compare.
Enter the numbers for your choice.
The calculator gives the answer with the working and a check.
Formulas used
- a : b = c : x\ \Rightarrow\ x = \frac{bc}{a}
- \text{share} = T\times\frac{r_i}{\sum r}
- u = \frac{p}{q}
Worked example
With the default numbers in the calculator above:
- The ratio in lowest terms (divide every part by the highest common factor): 2 : 3 : 5 (the highest common factor was 6)
- Each part as a fraction of the whole: 2/10, 3/10, 5/10 (20 %, 30 %, 50 %)
- As a decimal ratio of the first to the second part: 0.666667
Change the numbers in the calculator to see the full working, every step, for your own case.
A second worked example
A different case, with these numbers: What do you want? Solve the proportion a : b = c : x; First number a 3; Second number b 4; Third number (a third part of the ratio, or c in the proportion; 0 = not used for simplify) 9.
- Cross multiply: a : b = c : x means ax = bc: 12
- Check: the two ratios are equal: 0.75 and 0.75
Common questions
How do I simplify a ratio?
Divide every part by the highest number that goes into all of them. 12 : 18 simplifies to 2 : 3.
How do I share an amount in a ratio?
Add up the parts to get the number of shares, divide the amount by it to get one share, and multiply by each part.
How do I find which offer is better value?
Divide each price by its quantity to get the price for each unit and choose the smaller.
Related calculators
Got a question about this? Ask an engineering question and get a plain-language answer with references.
Further reading: Any school mathematics text (ratio and proportion).
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