How to measure height of building without any scale

Measuring the height of a building without a scale can be done using indirect methods that rely on basic tools, geometry, or observations.

1. Shadow Method (Using Similar Triangles)

This method uses the shadow cast by the building and a known object (like a stick or yourself) to estimate height based on proportional triangles.

Steps:

Measure a reference object and its shadow:
- Find a straight stick or pole of known height (e.g., 1 meter) and place it vertically in the ground.
- Measure the length of the stick’s shadow on the ground (e.g., 2 meters).
Measure the building’s shadow:
- At the same time of day (to ensure the sun’s angle is consistent), measure the length of the building’s shadow from its base to the tip of the shadow.

Tips:

Ensure measurements are taken at the same time to avoid changes in the sun’s angle.
Use a flat surface for accurate shadow measurements.
A tape measure or pacing can estimate shadow lengths if no ruler is available.

2. Angle of Elevation Method (Using a Clinometer or Smartphone)

This method uses trigonometry to calculate the height based on the angle of elevation from a known distance.

Steps:

Create or use a clinometer:
- Make a simple clinometer using a protractor, straw, string, and a weight (e.g., a small rock). Attach the weight to the string, tie it to the protractor’s center, and use the straw to sight the building’s top.
- Alternatively, use a smartphone app (many free apps measure angles using the device’s sensors).
Measure the angle of elevation:
- Stand a known distance from the building’s base (e.g., 50 meters). Measure this distance by pacing or using a tape measure.
- Look through the clinometer or smartphone app to the top of the building and record the angle of elevation (e.g., 30 degrees).
Measure your eye height:
- Note the height from the ground to your eyes (or the clinometer’s position), typically around 1.5–1.7 meters for an adult.
Calculate the height:
- Use the tangent function: $encoding="application/x-tex">\text{Building height above eye level} = \text{Distance to building} \times \tan(\text{angle of elevation})</annotation></semantics></math>$
- Add your eye height to get the total building height.

Tips:

Ensure the ground is level for accurate distance measurement.
Use a calculator for the tangent function (most smartphones have one).

3. Mirror Method

This method uses a mirror to create a line of sight to the building’s top, leveraging reflection and geometry.

Steps:

Place a mirror on the ground:
- Put a small mirror flat on the ground at a known distance from the building’s base (e.g., 10 meters).
Position yourself:
- Walk backward until you can see the top of the building reflected in the mirror when looking down.
- Measure the distance from your position to the mirror (e.g., 2 meters).
Measure your eye height:
- Note the height from the ground to your eyes (e.g., 1.5 meters).
Calculate the height:
- The ratio of your eye height to your distance from the mirror equals the ratio of the building’s height to its distance from the mirror.

Tips:

Ensure the mirror is flat and the ground is level.
This method works best for shorter buildings due to practical distance limitations.

4. Pencil Method (Using Perspective)

This is a rough estimation method using a pencil or similar object held at arm’s length.

Steps:

Hold a pencil at arm’s length:
- Stand a known distance from the building (e.g., 50 meters).
- Hold a pencil vertically at arm’s length so that it appears to match the height of the building in your field of vision.
Measure the pencil’s apparent height:
- Mark or note the portion of the pencil that aligns with the building’s height (e.g., 5 cm).
Measure your arm’s length:
- Measure the distance from your eye to the pencil (typically 50–60 cm for an adult).
Calculate the height:
- Use similar triangles: The ratio of the pencil’s marked length to your arm’s length equals the ratio of the building’s height to the distance to the building.

Tips:

This method is less accurate but requires minimal tools.
Ensure you keep the pencil steady and your arm fully extended.

5. Using a Reference Object of Known Height

If you know the height of a nearby object (e.g., a lamppost, a person, or a floor of the building), you can estimate the building’s height by comparison.

Steps:

Identify a reference object:
- Find an object with a known height (e.g., a lamppost known to be 3 meters tall or estimate a floor height at ~3 meters for a typical building).
Count or compare:
- Visually estimate how many times the reference object’s height fits into the building’s height.

Tips:

This method is less precise but useful when no tools are available.
Confirm the reference height if possible (e.g., check building standards for floor height).