# Scale Calculator - Map Scale, Model Scale & Drawing Scale

> Map distance ↔ real distance for any scale, find the scale from two lengths, 1:24, 1:64 and HO 1:87 model sizes, drawing scales, print DPI and area scale.

- URL: https://qilingtools.com/en/math/scale
- Category: Math Tools (https://qilingtools.com/en/math)
- Tags: [Math](https://qilingtools.com/en/tags/math), [Education](https://qilingtools.com/en/tags/education), [Design](https://qilingtools.com/en/tags/design)
- Last updated: 2026-10-26
- Price: Free, no sign-up
- Privacy: Runs locally in the browser; files are never uploaded

A scale is the ratio of a distance on a map, drawing or model to the real distance: 1:50000 means 1 cm on the map stands for 50,000 cm, or 500 m, on the ground. This calculator brings the common scale problems together. Map scale solves for any one of real distance, map distance or scale from the other two, converts the units for you (both sides of a ratio scale must use the same unit), and shows the verbal scale and a worked example. Drawing scale covers 1:50, 1:100 and enlargements like 2:1, plus imperial architectural scales such as 1/4" = 1’-0" (1:48). Model scale includes the usual ratios from 1:6 to 1:700, with O, OO, HO (1:87), N and Z gauges; enter a length, width and height to get model dimensions (or go from model back to real) and compare one object across every scale. Image / print size converts between pixels and millimetres or inches at any DPI, with A4, Letter and photo paper presets. Area scale shows why areas scale with the square of the ratio and volumes with the cube, and converts map areas into hectares, acres or square kilometres.

## How to use

1. Choose a mode: map scale, drawing scale, model scale, image / print size or area scale
2. Enter the scale (1:50000, 1cm=500m or 1/4" = 1’-0" all work) or pick a common one, and choose what to solve for
3. Enter the known distance or size with its unit and read the result, the other units and the worked example

## Features

- Map scale: solve for real distance, map distance or the scale itself
- Scales written as 1:50000, 1/50000, 1cm=500m, 1 in = 1 mi or 1/4" = 1’-0"
- Metric, imperial, nautical miles and Chinese li with automatic conversion
- Verbal scale and a worked example with your numbers
- Drawing scales for reductions and enlargements (2:1, 5:1) plus architectural and engineering imperial scales
- Model scales 1:6 to 1:700 including O, OO, HO, N and Z gauges, with a comparison table
- Print size: pixels ↔ mm / inches, pixels needed or effective DPI, with paper presets
- Area and volume scale factors with hectares, acres, square kilometres and mu

## FAQ

### How do you convert map distance to real distance?

Real distance = map distance × scale denominator, map distance = real distance ÷ scale denominator, and scale = map distance : real distance. The units must match: on a 1:50,000 map, 3.5 cm is 3.5 × 50,000 = 175,000 cm = 1.75 km. Going the other way, 1.75 km is 175,000 cm, divided by 50,000 gives 3.5 cm. If 2 cm on a map is 1 km on the ground, the scale is 2 cm : 100,000 cm = 1 : 50,000.

### Which is a larger scale, 1:50,000 or 1:10,000?

A scale is a fraction, and 1/10,000 is bigger than 1/50,000, so 1:10,000 is the larger scale. Larger-scale maps cover a smaller area in more detail — street plans are often 1:5,000 to 1:10,000 — while small-scale maps such as a national map at 1:4,000,000 cover a large area with less detail.

### What do 1:24, 1:64 and HO scale mean for models?

A model scale tells you what fraction of the real size the model is. 1:24 is common for car models, so a 4.8 m car becomes about 20 cm long; 1:64 die-cast cars are about 7.5 cm. HO is the most popular model railway scale at 1:87, O gauge is 1:48, N is 1:160 and Z is 1:220. Areas shrink by k² and volumes (or weight for the same material) by k³, so a 1:24 model has 1/13,824 of the real volume.

### Why is the area scale the square of the map scale?

Area is length times width, and both are reduced by the same factor k, so the area is reduced by k × k = k². On a 1:50,000 map the area ratio is 1 : 2,500,000,000, so 12 cm² on the map is 12 × 2.5 billion cm² = 300 hectares = 3 km². Volume is reduced by k³. To go from a real area to a map area, divide by the square of the scale denominator.

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