Proportional scale is how maps, models and drawings shrink or enlarge real life without changing its shape. A scale of 1:50 means 1 cm on the drawing stands for 50 cm in real life. Use this calculator to find a scaled length, a real length or the scale factor itself — all from the same proportion.
Proportional Scale Calculator
Scale 1 : N — fill in any two values.
Example: a 500 cm wall at 1:50 is 10 cm on the drawing. Use the same units for both lengths.
What Is Proportional Scale?
A proportional scale is the ratio between a drawing or model and the real object it represents. On a map with a scale of 1:25,000, 1 cm on the map is 25,000 cm — 250 metres — on the ground. On a model train at 1:87, every part is 1/87 of the real train. The scale keeps every length in the same proportion, so the shape never distorts.
How to Read a Scale: 1:50, 1:100 and Map Scales
Write a scale as 1:N, where N is how many real units one drawing unit stands for. At 1:50, divide the real length by 50 to get the drawing length, or multiply the drawing length by 50 to get the real length. At 1:100, a 12 m room is 12 cm on the plan. Map scales are often given as a bar scale too: if the bar says 1 cm = 2 km, then 3.5 cm on the map is 7 km on the ground.
Scale Factor: Enlarging and Reducing
The scale factor is the number you multiply by to go from real to drawing, or from one image to another. A scale factor of 1/50 reduces; a factor of 2 enlarges. When you enlarge a shape by a factor of 2, its lengths double but its area grows by 2² = 4 times. That is why scale drawings and similar figures are a core part of proportional reasoning in 10th grade.
Worked Examples
Example 1: A wall is 500 cm long. On a 1:50 plan it is 500 ÷ 50 = 10 cm. Example 2: A map distance of 4 cm at 1:25,000 is 4 × 25,000 = 100,000 cm = 1 km. Example 3: A model car is 6 cm long and the real car is 4.2 m (420 cm). The scale is 420 ÷ 6 = 70, so the model is 1:70.
Proportional Scale FAQs
What does a scale of 1:100 mean?
1 unit on the drawing stands for 100 of the same units in real life. A 12 m room is 12 cm on a 1:100 plan.
How do you find the real length from a scale drawing?
Multiply the drawing length by the scale number N. A 10 cm drawing at 1:50 is 10 × 50 = 500 cm, or 5 m, in real life.
What is the difference between scale and scale factor?
They describe the same idea. The scale 1:50 says the drawing is 1/50 of real life; the scale factor from real to drawing is 1/50, and from drawing to real it is 50.
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