Scale Factor Calculator
Find the scale factor between a real object and its model, drawing, map or enlargement. Enter the two lengths in any units — feet and inches, kilometers and centimeters — and get the multiplier, the ratio such as 1:48, and how areas and volumes scale.
- Scale ratio (scaled : original)
- 1:48
- Scaled size as a percent
- 2.0833%
- Area factor (scale²)
- 0.000434
- Volume factor (scale³)
- 0.000009
Saved setups
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Your recent calculations
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Formula
How to use it
- Enter the original (real) length and pick its unit.
- Enter the matching length on the model, drawing or copy and pick its unit.
- Read the scale factor and the ratio. A factor below 1 is a reduction; above 1 is an enlargement.
Worked examples
A 24 ft boat built as a 6 in model
- Scale factor (scaled ÷ original)
- 0.020833
- Scale ratio (scaled : original)
- 1:48
- Scaled size as a percent
- 2.0833%
A map where 2 cm stands for 1 km
- Scale factor (scaled ÷ original)
- 0.00002
- Scale ratio (scaled : original)
- 1:50000
Enlarging a 4 in photo edge to 10 in
- Scale factor (scaled ÷ original)
- 2.5
- Scale ratio (scaled : original)
- 2.5:1
- Area factor (scale²)
- 6.25
- Volume factor (scale³)
- 15.625
Common scales
Architectural drawings in the US often use 1/4 inch to the foot, which is 1:48, or 1/8 inch to the foot, 1:96. Model railroads use about 1:87 for HO and 1:160 for N. Die-cast cars are commonly 1:18, 1:24 or 1:64. USGS topographic maps at 1:24,000 show 2,000 feet to the inch.
Area and volume scale faster than length
Doubling every length makes the area 4 times and the volume 8 times as large. Going the other way, a 1:48 model has 1/2,304 of the surface area and 1/110,592 of the volume of the real thing — which is why a model needs so little paint.
The two lengths must be converted to the same unit before dividing. The unit menus do that for you.
Questions people ask
What is the scale of a 6-inch model of a 24-foot boat?
1:48. 24 feet is 288 inches, and 288 ÷ 6 = 48, so the scale factor is about 0.0208.
What is the scale factor when a 4-inch photo is enlarged to 10 inches?
2.5, or 250%. The area becomes 6.25 times as large.
If 2 cm on a map is 1 km on the ground, what is the scale?
1:50,000. One kilometer is 100,000 cm, and 100,000 ÷ 2 = 50,000.