Calculadora de Formas Similares
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
lados ∝ k ; áreas ∝ k² ; volumes ∝ k³
About this calculator
The Similar Shapes Calculator is an online tool that applies the principle of similarity ratio between two geometric figures. When two shapes are similar, their linear dimensions (such as sides, heights, or radii) maintain a constant proportion k. This means that if one dimension of the larger figure is k times the corresponding dimension of the smaller figure, then areas are multiplied by k² and volumes by k³. The calculator allows you to enter a linear dimension, area, or volume of one figure and the scale factor k, and it automatically calculates the corresponding values in the other figure.
The operation is simple: you choose the type of measurement (linear, area, or volume), enter the known value and the scale factor k (for example, 2 if the larger figure is twice the smaller). The calculator then applies the correct formula: for linear dimensions, multiply or divide by k; for areas, by k²; and for volumes, by k³. The result is displayed instantly, making it easy to compare the two figures without manual calculations.
Use this calculator in everyday situations, such as when enlarging or reducing technical drawings, scale models, or architectural models. For example, if you have a 1:50 scale model and want to know the real area of a wall, simply enter the model's area and the factor k=50. It is also useful in school geometry problems, when calculating volumes of similar solids, or in graphic design for resizing images while maintaining proportion.
Important precautions: ensure the figures are truly similar (same shape, equal angles). The factor k must be positive; if k is less than 1, the second figure is smaller. Remember that the formula only applies to corresponding measurements: do not mix sides with areas or volumes in the same comparison. Also check units: if you enter an area in cm², the result will be in cm²; for volumes, in cm³.
Frequently asked questions
How do I calculate the area of a similar figure from a linear dimension?
If you know a linear dimension (like side) of the original figure and the scale factor k, first calculate the linear dimension of the similar figure (multiply by k). Then, for area, multiply the original area by k².
What happens if the scale factor k is a fraction, like 0.5?
If k is 0.5, the similar figure is smaller. Linear dimensions are half the original, area is 0.25 times (k²), and volume is 0.125 times (k³) the original.
Can I use this calculator for 3D shapes?
Yes, it works for any three-dimensional figure as long as the shapes are similar. Just select the volume option and enter the known value.
What is the difference between linear scale factor and area scale factor?
The linear scale factor (k) applies to lengths. The area scale factor is k², and the volume scale factor is k³. The calculator automatically applies the correct power based on the measurement type.
Do I need to use the same units for both figures?
Yes, units must be consistent. If you enter a measurement in meters, the result will be in meters (for linear), square meters (for area), or cubic meters (for volume).