Scale Factor Calculator
The Scale Factor Calculator determines the multiplier between two measurements. Enter original and scaled dimensions to find the scale factor, or apply a known factor to compute new sizes. Ideal for architectural blueprints, model building, map reading, and resizing artwork.
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What is a Scale Factor?
A scale factor is the ratio between a scaled measurement and the corresponding original measurement. If a 12-meter wall is represented as 6 cm on a blueprint, the scale factor is 6/1200 = 1/200, or 1 : 200. The scale factor tells you how many times larger or smaller the representation is compared to reality.
Scale factors are used in architecture (floor plans), cartography (maps), model engineering (miniature replicas), photography (enlargements and reductions), and geometry (similar triangles). A scale factor greater than 1 means enlargement; less than 1 means reduction.
Използвани Формули и Уравнения
Този калкулатор използва 5 основни уравнения:
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.
Как се Използва този Калкулатор
За да използвате този Калкулатор за Отношения, следвайте 3 лесни стъпки:
Въведете Данни
Въведете известните стойности на съотношението в полетата за въвеждане. Оставете едно поле празно — това е неизвестното, което калкулаторът ще реши.
Изберете Режим
Изберете режим на съотношение — Реши, Опрости или Мащабирай. Всеки режим прилага различни уравнения към вашите входни стойности.
Получете Резултати
Кликнете върху Пресметни. Екранът с резултати показва отговора с цветна скала, кръгова диаграма и пошагово решение.
Примерни Задачи с Решения Стъпка по Стъпка
Ето 3 практически примера с подробно математическо обяснение на стъпките:
Вход 1 Find scale factor: 5 cm model of a 10 m building
Вход 2 Scale a 15 m room to 1:50 blueprint
Вход 3 Find real distance from a map measurement of 8 cm at 1:25000
Често Задавани Въпроси
How do you find the scale factor between two objects? ▼
Divide any measurement of the scaled object by the corresponding measurement of the original. If the model is 4 cm and the real object is 8 m (800 cm), the scale factor is 4/800 = 1/200 or 1 : 200.
What does a scale factor of 2 mean? ▼
A scale factor of 2 means the new object is twice the size of the original. Every dimension is multiplied by 2 — a 5 cm line becomes 10 cm, a 3 cm width becomes 6 cm.
What is the difference between scale factor and ratio? ▼
A scale factor is a specific type of ratio that compares a scaled representation to the original. While all scale factors are ratios, not all ratios are scale factors — ratios can compare any two quantities.
How do architects use scale factors? ▼
Architects use scale factors like 1:100 or 1:50 to draw buildings at reduced sizes on paper. At 1:100, every 1 cm on the plan represents 100 cm (1 meter) in reality. This allows entire buildings to fit on standard drawing sheets.
Can scale factors be greater than 1? ▼
Yes. Scale factors greater than 1 represent enlargement. A microscope image at 400× has a scale factor of 400:1, meaning the image is 400 times larger than the actual specimen.