Calculate a volume scale factor from a linear scale like 1:24 or from two volumes, or scale an original volume into liters, gallons and more.

Enter 1:24, 0.5 or 2. All lengths must use the same scale.

Common linear scale

Related Calculators

Volume Scale Factor Formula

The following formula is used to calculate the scaled volume.

SV = OV × SF³

Variables:

  • SV is the scaled volume (units³)
  • OV is the original volume (units³)
  • SF is the scale factor (dimensionless)

To calculate the scaled volume, multiply the original volume by the cube of the scale factor.

What is a Volume Scale Factor?

A volume scale factor is the ratio of new volume to original volume. For geometrically similar objects, it equals the cube of the linear scale factor (new length divided by original length). Thus a 1:24 linear scale gives a 1:13,824 volume ratio. All three lengths must scale equally.

How to Calculate Scaled Volume?

The following steps outline how to calculate the Scaled Volume.

  1. First, determine the original volume (OV) in cubic units.
  2. Next, determine the scale factor (SF).
  3. Next, gather the formula from above = SV = OV * SF³.
  4. Finally, calculate the Scaled Volume (SV) in cubic units.
  5. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

original volume (OV) = 8 units³

linear scale factor (SF) = 2; scaled volume = 8 × 2³ = 64 units³