Fraction Calculator
Add, subtract, multiply and divide fractions: with the working shown, so you can follow the method rather than just take the answer.
Every result also shows the millimetre equivalent, because in Canada you will often need both.
Fraction Calculator Canada
Add, subtract, multiply, and divide fractions with simplified and mixed number results.
23 / 20
1 3/20
1.15
The Four Operations
Adding and subtracting
Both need a common denominator. You can only add parts of the same size.
Finding it: multiply denominators together, or use lowest common multiple. For 1/2 and 1/3, multiplying gives 6, which is also the lowest.
Multiplying
Straight across: no common denominator needed.
Multiply numerators, multiply denominators, and then simplify to lowest terms.
Dividing
Flip the second fraction and multiply.
That reads clearly when you ask the question behind it: how many quarters fit into one half? Two.
Simplifying and Mixed Numbers
Simplifying
Divide both numbers by their greatest common divisor (GCD).
A fraction is fully simplified when the only number dividing both parts is 1.
Mixed to improper
Multiply whole number by denominator, add numerator, keep denominator.
Improper fractions make multiplication, division, and automated math significantly easier.
Improper to mixed
Divide numerator by denominator to find whole units and remainder.
Which form to use: improper fractions are easier to calculate with; mixed numbers are easier to read on tape measures.
Fractions to Decimals and Back
Fraction to decimal
Divide the top by the bottom.
Some divide cleanly; others repeat. 1/3 = 0.333… and never terminates.
Decimal to fraction
Put the decimal over a power of ten, then simplify.
Reduces directly to simplest terms through common divisors.
Nearest usable fraction
Practical measuring from decimal or millimetre readings.
About 0.5 mm under. Our calculator resolves precision to the nearest 1/16", 1/32" or 1/64".
Fractional Inches to Millimetres
One inch is exactly 25.4 millimetres (defined, not approximate) so every fractional inch converts exactly.
| Fraction | Decimal Inch | Millimetres (mm) |
|---|---|---|
| 1/16" | 0.0625 | 1.5875 |
| 1/8" | 0.125 | 3.175 |
| 3/16" | 0.1875 | 4.7625 |
| 1/4" | 0.25 | 6.35 |
| 5/16" | 0.3125 | 7.9375 |
| 3/8" | 0.375 | 9.525 |
| 7/16" | 0.4375 | 11.1125 |
| 1/2" | 0.5 | 12.7 |
| 9/16" | 0.5625 | 14.2875 |
| 5/8" | 0.625 | 15.875 |
| 11/16" | 0.6875 | 17.4625 |
| 3/4" | 0.75 | 19.05 |
| 13/16" | 0.8125 | 20.6375 |
| 7/8" | 0.875 | 22.225 |
| 15/16" | 0.9375 | 23.8125 |
| 1" | 1.0 | 25.4 |
1/4" ≈ 6.35 mm and 1/2" = 12.7 mm. From those two you can estimate most others quickly.
25 mm is just under 1", close enough for rough work (0.4 mm out), but not close enough for joinery.
Why Canada Uses Both Systems
If you have ever had a metric plan and imperial lumber on the same job, this is why.
Canada has been officially metric since 1970. Gas comes in litres, distances in kilometres, temperature in Celsius.
But construction runs largely on imperial, and the reason is structural rather than cultural. The materials supply chain runs north to south from US mills and factories. Lumber, plywood, drywall, fasteners and tape measures all arrive dimensioned in inches, because that is how they are manufactured on both sides of the border.
What that looks like in practice
And the two get mixed on a single drawing. A plan giving dimensions in millimetres and then specifying "2×6 framing at 16" o.c." is using both systems at once, which is common, and the main reason a conversion table is worth having to hand.
Even Natural Resources Canada publishes both. Its dimension lumber page describes widths "in multiples of 5 centimetres (2 inches)," and a two by four as "4 centimetres (1.5 inches) thick and 9 centimetres (3.5 inches) wide."
The same everywhere in Canada
British Columbia and Alberta each maintain their own building code, derived from the National Building Code and written in metric. The materials arriving on site are imperial.
So a renovation in Vancouver, Burnaby, Surrey, Richmond or Victoria works to a metric BC code with imperial lumber, and one in Calgary, Edmonton, Red Deer, Lethbridge, Medicine Hat, Airdrie, Cochrane, Canmore, Banff or Okotoks works to a metric Alberta code with the same imperial lumber.
The split is identical across the country, which is exactly why a conversion chart is more useful here than almost anywhere else.
Reading a Tape Measure
Imperial tapes divide each inch into sixteenths, with line length indicating the fraction:
| Line Length | Fraction Indicated |
|---|---|
| Longest (numbered) | The full inch |
| Next longest | 1/2" |
| Next | 1/4" and 3/4" |
| Next | eighths: 1/8, 3/8, 5/8, 7/8 |
| Shortest | sixteenths (1/16 increments) |
The method: count sixteenths from the last inch mark, then simplify.
Why measurements land on awkward fractions: because the marks are sixteenths. A measurement of 7/16" is not unusual; it is just one mark short of a half.
Many Canadian tapes are dual marked, inches on one edge and centimetres on the other. That is a direct product of the hybrid system, and worth using rather than converting by hand.
For finer work, some tapes and rules go to 32nds or 64ths. Our calculator converts to all three.
Nominal vs Actual Lumber
A 2×4 is not 2" × 4". It is 1 1/2" × 3 1/2".
The nominal name refers to the rough sawn size before the board is dried and planed. What you buy is the finished size.
| Nominal Size | Actual Finished Size |
|---|---|
| 1×4 | 3/4" × 3 1/2" |
| 2×4 | 1 1/2" × 3 1/2" |
| 2×6 | 1 1/2" × 5 1/2" |
| 2×8 | 1 1/2" × 7 1/4" |
| 2×10 | 1 1/2" × 9 1/4" |
| 2×12 | 1 1/2" × 11 1/4" |
| 4×4 | 3 1/2" × 3 1/2" |
The rule, and the catch
Boards up to 6" nominal lose 1/2" in width. At 8" nominal and above, the loss increases to 3/4".
So a 2×6 is 5 1/2", but a 2×8 is 7 1/4", not 7 1/2". That change catches people, and it is the most common lumber dimension error.
Thickness on all 2× dimension lumber is 1 1/2".
Canadian and American lumber are identical
Both countries follow Voluntary Product Standard PS 20, maintained by the American Lumber Standard Committee and recognised in Canada. A 2×4 from a Canadian mill has the same actual dimensions as an American one.
One exception: rough sawn or full dimension lumber, sold undressed, genuinely measures its nominal size. If you have bought rough 2×4s and they measure 2" × 4", that is expected.
Worked Examples From the Trades
Three calculations where the fractions do real work.
Joist plus subfloor
2×10 joist (9 1/4") + 3/4" plywood subfloor
Clean whole number result, which is why that combination is so widely used in residential framing.
Framed wall thickness
2×4 stud (3 1/2") + 1/2" drywall on each side
Not 5", which is what you would get using the nominal 4" stud width. That half inch difference matters for door jambs and trim.
Why insulation batts are 14 1/2" wide
Spacing calculations between stud bays:
Which is exactly the width batts are sold in. Once you have seen the arithmetic, the sizing stops looking arbitrary.
Common Mistakes
- »Adding numerators and denominators separately. 1/2 + 1/3 is not 2/5. You need a common denominator.
- »Forgetting to simplify. 6/12 is arithmetically correct, but 1/2 is clearer and standard.
- »Using nominal dimensions in framing calculations. A 2×4 wall is 3 1/2" deep, not 4".
- »Assuming width reduction is uniform across all lumber. It is 1/2" up to 6" nominal, and 3/4" from 8" up.
- »Mixing nominal and actual in the same sum. If you are adding joist depth to subfloor thickness, both must be actual finished dimensions.
- »Rounding millimetre conversions too early. 25.4 mm per inch is exact; carry the decimals through and round at the very end.
- »Trusting the label on plywood. Sheet goods sold under imperial names are often manufactured to metric thicknesses. When tolerance matters, measure the material directly.
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Open toolFraction Frequently Asked Questions
Method and Sources
Method: Standard fraction arithmetic with the working shown at each step. Conversions use the exact definition of one inch as 25.4 millimetres, so fractional inch values convert without rounding error.
Sources: Lumber dimensions follow Voluntary Product Standard PS 20, maintained by the American Lumber Standard Committee and recognised in Canada. Dimension lumber descriptions also reference Natural Resources Canada.
On measurement conventions: Building material dimensions and conventions occasionally change, and sheet goods in particular may be manufactured to metric thicknesses while sold under imperial names. When tolerance matters, measure the actual material rather than relying on the label.
Lumber dimensions verified September 2026. Disclaimer: CalcVault provides mathematical and trade conversion calculations for educational and informational purposes.
Appendix A: Update Checklist
This page is close to maintenance free. Never changes: all fraction arithmetic, the inch to millimetre table (25.4 mm has been the defined conversion since 1959), the worked trades examples, and tape measure divisions.
Figures that interlock: recompute only if a standard changes: nominal vs actual table, joist plus subfloor (9 1/4 + 3/4 = 10"), wall thickness (3 1/2 + 1/2 + 1/2 = 4 1/2"), insulation batt widths (14 1/2" and 22 1/2"), and every FAQ containing a dimension.