Scale Factor Calculator
Calculate scale factors between actual and scaled dimensions for maps, architectural models, engineering blueprints, and miniature models. Enter any two measurements to find the exact scale ratio, or apply a known scale to convert between real-world and scaled sizes.
🕐 Recent Calculations
What is a Scale Factor?
A scale factor is the ratio between a scaled representation and the actual object it represents. A 1:100 architectural scale means 1 centimeter on the drawing represents 100 centimeters (1 meter) in reality. A 1:24 model car means the model is 1/24th the size of the real vehicle. Scale factors enable accurate proportional representation of objects that are too large (buildings, maps) or too small (cells, circuits) to work with at actual size.
Scale factors are used in architecture (1:50, 1:100, 1:200 drawings), engineering (full-size, half-scale prototypes), cartography (1:25,000 to 1:1,000,000 maps), model building (1:24, 1:48, 1:72 miniatures), 3D printing (scaling models to fit print beds), and photography (macro magnification ratios like 2:1 or 1:1). Understanding scale factors ensures accurate measurement, planning, and fabrication across all these disciplines.
적용 수학 공식 및 방정식
이 Scale Factor Calculator는 5가지 핵심 수학 공식을 사용합니다:
1 Scale Factor Calculation ▼
Divide the new measurement by the original measurement. A 3 cm model of a 6 m object has a scale factor of 3/600 = 1/200.
2 Scaled Size from Factor ▼
Multiply the original measurement by the scale factor. A 10 m wall at 1:50 scale = 10 × (1/50) = 0.2 m = 20 cm.
3 Original Size from Scaled ▼
Divide the scaled measurement by the scale factor. A 4 cm line on a 1:100 map = 4 / (1/100) = 400 cm = 4 m.
Explore all calculation options on the 비율 계산기 home page.
비율 계산기 사용법
이 비율 계산기는 아래의 3단계로 쉽게 사용할 수 있습니다:
수치 입력하기
입력 칸에 알고 있는 비율 값을 입력합니다. 구하려는 미지수 자리의 칸 하나는 비워둡니다.
모드 선택하기
비율 모드(풀기, 간소화, 스케일링)를 선택합니다. 각 모드는 입력한 수치에 맞춰 다른 공식들을 적용합니다.
결과 확인하기
계산하기 버튼을 누릅니다. 결과 화면에 정답과 함께 시각적인 비율 바, 원형 차트, 상세한 단계별 풀이 과정이 출력됩니다.
실제 예제 문제 및 단계별 풀이
비율 계산기를 활용하여 아래 3가지 예제 문제를 단계별로 해결하는 과정입니다:
입력 1 Find scale factor: 5 cm model of a 10 m building
입력 2 Scale a 15 m room to 1:50 blueprint
입력 3 Find real distance from a map measurement of 8 cm at 1:25000
자주 묻는 질문 (FAQ)
How do I calculate a scale factor? ▼
Scale Factor = Scaled Size ÷ Actual Size. If a 5-meter wall is represented as 50mm on a drawing: Scale = 50mm ÷ 5000mm = 1/100, or 1:100. If a model car is 200mm and the real car is 4800mm: Scale = 200/4800 = 1/24, or 1:24.
What does 1:100 scale mean? ▼
1:100 means 1 unit on the drawing or model represents 100 of the same units in real life. So 1cm on paper = 100cm (1 meter) actual. A 12-meter-long building would be drawn as 120mm on a 1:100 blueprint.
How do I convert between different scales? ▼
Multiply by the ratio of the two scales. To convert a 1:50 drawing to 1:100: multiply all dimensions by 50/100 = 0.5 (halve them). To convert 1:100 to 1:50: multiply by 100/50 = 2 (double them).
What is the most common architectural scale? ▼
In metric countries, 1:50 and 1:100 are most common for building plans. In the US, common scales are ¼" = 1'-0" (1:48) and ⅛" = 1'-0" (1:96) for floor plans, and 1½" = 1'-0" (1:8) for construction details.
How does scale factor affect area and volume? ▼
Area scales by the square of the linear factor: 1:10 linear = 1:100 area. Volume scales by the cube: 1:10 linear = 1:1000 volume. A 1:10 scale model building has 1/100th the floor area and 1/1000th the interior volume of the actual building.
What scale do Google Maps use? ▼
Google Maps uses dynamic scaling — the scale changes as you zoom. Each zoom level approximately halves the scale. At zoom level 15 (street level), the scale is approximately 1:4,500. At zoom level 10 (regional), approximately 1:150,000. The scale bar on the map shows the current scale.
How do I calculate actual distance from a map? ▼
Measure the distance on the map, then multiply by the scale denominator. On a 1:25,000 map, a 4cm measured distance = 4 × 25,000 = 100,000cm = 1km actual ground distance.
What is a representative fraction in cartography? ▼
A representative fraction (RF) is the map scale expressed as a ratio, like 1:25,000. It means 1 unit on the map = 25,000 of the same units on the ground. RF is unit-independent: 1cm = 25,000cm = 250m, or 1 inch = 25,000 inches ≈ 694 yards.
How do I scale a 3D model for 3D printing? ▼
Divide the desired model size by the original model size and multiply by 100 to get the slicer percentage. If the original STL is 300mm tall and your print bed fits 150mm: 150/300 × 100 = 50%. Scale uniformly (all axes at 50%) to maintain proportions.
What scale are common model kits? ▼
Aircraft: 1:72 (most popular), 1:48, 1:32. Cars: 1:24, 1:25, 1:43, 1:18. Military vehicles: 1:35 (standard), 1:72. Ships: 1:350, 1:700. Trains: HO 1:87, N 1:160, O 1:48, G 1:22.5. Dollhouses: 1:12 (most common).