Formulas and sources
Each formula this calculator uses, where it comes from, and what it leaves out. "How it works" shows the same formula with your own numbers.
Simplify
Simplify mode
- A
- the first term
- B
- the second term
GCD is the greatest common divisor of the two terms. Decimal terms are first multiplied by the same power of ten to make them whole, so 0.5:1.5 becomes 5:15 and then 1:3, and the common factor is shown in the units you typed (0.5). A term may have up to 12 decimal places.
Source: Uses Euclid’s algorithm as NIST’s Dictionary of Algorithms and Data Structures gives it [1]; the greatest common factor as in the Common Core State Standards for Mathematics, 6.NS.B.4 [2]. Scaling decimal terms to whole numbers is CalcTrail’s own.
Scale
Scale mode
- A
- the first term
- B
- the second term
- f
- the factor
Both terms are multiplied by the same factor, so the value A ÷ B does not change. Each scaled term is rounded to 6 decimal places. The table beside the answer shows the ratio at 1, 2, 3, 4, 5 and 10 times.
Source: Standard formula; no single publisher. Tables of equivalent ratios as in the Common Core State Standards for Mathematics, 6.RP.A.3.a [2].
Solve a proportion
Solve mode
- A
- the first term
- B
- the second term
- C
- the third term
- D
- the fourth term
The unknown term is isolated by division, for example D = (B × C) ÷ A, so 2:3 = 8:D gives D = 12.
Source: Standard formula; no single publisher. Proportional relationships as in the Common Core State Standards for Mathematics, 7.RP.A.2 [2].
Compare
Compare mode
- A
- the first term of ratio 1
- B
- the second term of ratio 1
- C
- the first term of ratio 2
- D
- the second term of ratio 2
Cross-products that differ by less than one part in a billion of the larger one count as equal, so rounding in the arithmetic does not split equal ratios: 0.1:0.3 and 1:3 are equivalent. The working says when this applies.
Source: Standard formula; no single publisher. Testing for equivalent ratios as in the Common Core State Standards for Mathematics, 7.RP.A.2.a [2]. The tolerance is CalcTrail’s own.
Convert
Convert mode
- A
- the first term
- B
- the second term
A ÷ B is the value of the ratio. The percent is A ÷ B × 100, B’s share is B ÷ (A + B), and the fraction is the ratio in lowest terms, as Simplify finds it.
Source: Uses the definitions in the Common Core State Standards for Mathematics, 6.RP.A.2 and 6.RP.A.3.c [2], and the “value of the ratio” of the Progressions, p. 157 [3].
Mix, solving Quantity B
Mix mode, when Calculate This is Quantity B
- A
- the first part of the ratio
- B
- the second part of the ratio
The known quantity is converted to milliliters first: 1 US gallon is 3,785.411784 mL and 1 US fluid ounce is 29.5735295625 mL. So 32:1 with 5 US gallons of fuel needs 20 US fluid ounces of oil.
Source: Standard proportion; no single publisher. Uses the US gallon and fluid ounce of NIST Handbook 44, Appendix C [4].
Mix, solving Quantity A
Mix mode, when Calculate This is Quantity A
- A
- the first part of the ratio
- B
- the second part of the ratio
Source: Standard proportion; no single publisher. Fuel ratios: STIHL [5], Husqvarna [6] and Troy-Bilt [7], each for its own equipment.
Split
Split mode
Each allocation shows 4 decimal places on the card, in How it works, in copy and in export, so the rounded parts can differ from the total: 1:1:1 of 100 shows 33.3333 three times. Glue and starch 3:2 that make 85 cups split into 51 and 34.
Source: Standard formula; no single publisher. The tape-diagram steps of the Progressions, p. 162 [3].
Sources
- National Institute of Standards and Technology. Dictionary of Algorithms and Data Structures: Euclid’s algorithm. Entry modified March 2, 2015.
- National Governors Association Center for Best Practices and Council of Chief State School Officers. Common Core State Standards for Mathematics, standards 6.RP.A.1 to 6.RP.A.3, 6.NS.B.4, 7.RP.A.2 and 7.RP.A.3. 2010.
- Common Core Standards Writing Team. Progressions for the Common Core State Standards for Mathematics, Ratios and Proportional Relationships, grades 6 to 7, pp. 157 and 162. Institute for Mathematics and Education, University of Arizona, February 28, 2023.
- National Institute of Standards and Technology. NIST Handbook 44, Appendix C: General Tables of Units of Measurement, p. C-6 and the liquid-measure table on p. C-16: the US gallon and fluid ounce. 2026 edition.
- STIHL USA. How To Mix Oil & Gas Guide. Undated page, read October 5, 2026.
- Husqvarna. How to mix 2-stroke fuel. Undated page, read October 5, 2026.
- Troy-Bilt (MTD). How to Mix 2-Cycle/2-Stroke Engine Oil for Hand-held Equipment. Undated page, read October 5, 2026.
What this calculator does not cover
- Every term must be greater than zero, so a ratio such as 0:5 is refused. Simplify and Convert take terms of up to 12 decimal places, and every field takes up to 1,000,000,000,000.
- Mix converts between volume units only: US gallons, liters, US fluid ounces and milliliters. It has no weights and no imperial gallon.
- Simplify, Scale, Solve, Compare and Convert take two terms (four for Solve and Compare). A ratio of three or more terms uses Split, which needs a total.
- It has no aspect-ratio or golden-ratio presets; the Aspect Ratio Calculator works out screen and image sizes.
- It does not choose a fuel ratio for an engine; the ratio is in the engine’s manual. STIHL gives 50:1 for most of its gasoline equipment, and Husqvarna 50:1 for its products up to 75 cc. Troy-Bilt gives 32:1 for its handheld two-cycle equipment made before 2003 and 40:1 after 2002. The 16:1 chip is a plain ratio.
Sources checked on .