# Calculations

## Find the area of a log in cubic metres

1. Measure the diameter of one face (side to side) of the log.

2. Divide diameter by 2 to find the radius.

3. Use formula pi r2 to find area of the face

4. Repeat this for other end of the log

5. Add the two areas together, then divide by 2 to get an average area

6. Mulitply average area of the face by length of the log to get total area.

Example:

1. Diameter of end (A) is 0.80m wide

2. 0.80 / 2 = 0.40

3. Find area of the face = pi r2

A = 3.14 x (0.40×0.40)

A = 3.14 x (0.16)

A = 0/5024

4. Repeat this for the other end of the log (B)

A= 0.75 / 2 = 0.375

A= 3.14 x (0.375 x 0.375)

A= 3.14 x (0.140625)

A= 0.4416

5. Add the two areas together, then divide by 2 to get an average area

A= (0.5024 + 0.4416) / 2

A= 0.944 / 2

A= 0.472

6. Multiply average area of the face by length of the log to get total area

A= 0.472 x 4.5

A= 2.124 cubic metres.

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## Find the cubic meterage of sawn timber

Raw log to estimated sawn:

To find estimated sawn timber from raw log form, you must decide on a possible percentage recoverable, depending on:

– Log size (small logs, lower recovery)

– Log shape (odd shape, lower recovery)

– Log quality (rot, internal knots etc, lower recovery)

– Size of boards (small boards = more sawdust = lower recovery)

Recovery rates can float between 30% for extremely small, knotty, irregular logs, to around 85% for perfect medium to large logs.

Using an average of 65% for this exercise, multiply the area of the log by 65%.

Using theprevious example with a log areaof 2.124 cubic metres, x 65% = 1.3806.

So from an average log of over 2 cubic metres, you get just under 1.5 cubic metres of sawn timber.

Measuring Sawn Timber:

1. Obtain the end dimensions of the boards being cut (eg. 2″x4″ as shown)

2. Multiply the end dimensions by the length of the board

3. Multiply the total by the number of boards this size

4. Keep tallying all piles of similar boards, add them together for the total meterage of sawn timber

Example:

1. End dimensions = 0.10 x 0.05 = 0.005m

2. 0.005 x 4m (length) = 0.02m

3. 0.02m x 100 (eg number of boards) = 2 cubic metres in total.

Click here to use our board foot calculator & measurement converter.