How to Convert Decimal Degrees to Feet Calculator

Converting decimal degrees to feet is a common task in surveying, mapping, and construction. This guide explains the conversion process, provides a calculator, and offers practical examples.

What are decimal degrees?

Decimal degrees are a way to express geographic coordinates (latitude and longitude) as decimal numbers rather than degrees, minutes, and seconds. For example, 40.7128° N, 74.0060° W represents New York City's coordinates in decimal degrees.

Decimal degrees are commonly used in modern GPS devices, mapping software, and geographic information systems (GIS). They provide a more precise and easier-to-use format compared to the traditional degrees-minutes-seconds system.

Conversion formula

The conversion from decimal degrees to feet depends on the specific context, particularly the type of measurement you're converting. Here are the most common scenarios:

Latitude to Feet (North-South Distance)

To convert latitude decimal degrees to feet (distance along a meridian):

Feet = Decimal Degrees × 364,567.2

This formula assumes the Earth is a perfect sphere with a radius of 3,963.34 miles (6,378,160 meters).

Longitude to Feet (East-West Distance)

To convert longitude decimal degrees to feet (distance along a parallel):

Feet = Decimal Degrees × 364,567.2 × cos(Decimal Degrees × π/180)

This accounts for the fact that longitude lines converge at the poles.

Note: These formulas provide approximate distances. For precise measurements, especially over large areas, more complex calculations considering the Earth's ellipsoidal shape are recommended.

How to convert decimal degrees to feet

Follow these steps to convert decimal degrees to feet:

Identify whether you're converting latitude or longitude decimal degrees.
For latitude conversion, multiply the decimal degrees by 364,567.2.
For longitude conversion, multiply the decimal degrees by 364,567.2 × cos(decimal degrees × π/180).
Round the result to a reasonable number of decimal places for your application.

Example calculation

Let's convert 1° of latitude to feet:

1° × 364,567.2 = 364,567.2 feet

This means one degree of latitude is approximately 364,567.2 feet.

Example calculation for longitude

Convert 1° of longitude at 45° latitude:

1° × 364,567.2 × cos(45° × π/180) ≈ 1° × 364,567.2 × 0.7071 ≈ 256,440.5 feet

At 45° latitude, one degree of longitude is approximately 256,440.5 feet.

Practical applications

Converting decimal degrees to feet is useful in various fields:

Surveying and mapping: Converting GPS coordinates to linear measurements for land surveys.
Construction: Calculating distances between points for project planning.
Navigation: Estimating distances between locations for route planning.
Geographic research: Analyzing spatial relationships between locations.

Comparison table

Decimal Degrees	Latitude to Feet	Longitude to Feet (at Equator)	Longitude to Feet (at 45° Latitude)
1°	364,567.2	364,567.2	256,440.5
0.1°	36,456.72	36,456.72	25,644.05
0.01°	3,645.67	3,645.67	2,564.41

Common mistakes to avoid

When converting decimal degrees to feet, be aware of these common pitfalls:

Assuming equal distance: Forgetting that longitude degrees are shorter at higher latitudes.
Using incorrect formulas: Applying latitude formulas to longitude conversions.
Rounding errors: Not considering the appropriate number of decimal places for your application.
Ignoring context: Using the same conversion for both latitude and longitude without considering their different properties.

FAQ

How accurate is the decimal degrees to feet conversion?

The provided formulas give approximate results. For precise measurements, especially over large areas, more complex calculations considering the Earth's ellipsoidal shape are recommended.

Can I use the same formula for both latitude and longitude?

No, different formulas are needed. Latitude conversion uses a simple multiplication, while longitude conversion requires an additional cosine factor to account for the convergence of meridians.

What's the difference between decimal degrees and degrees-minutes-seconds?

Decimal degrees express coordinates as decimal numbers (e.g., 40.7128°), while degrees-minutes-seconds use separate values for degrees, minutes, and seconds (e.g., 40°42'46" N). Decimal degrees are more precise and easier to use in calculations.

How do I convert feet back to decimal degrees?

To convert feet back to decimal degrees, divide the feet value by 364,567.2 for latitude. For longitude, divide by 364,567.2 × cos(latitude in radians).