A Degrees ↔ Feet Calculator converts angular measurements (degrees) into linear distance (feet) along a circular path and vice versa. This conversion is essential in surveying, engineering, astronomy, and construction where angular displacement needs to be related to actual ground measurements.
Importance of Degrees to Feet Conversion:
- Used in Surveying & Land Measurement: Helps calculate curved distances on a circular path.
- Essential in Engineering & Construction: Determines arc lengths in structural and roadway designs.
- Vital in Astronomy & Navigation: Assists in converting celestial movements into measurable distances.
- Supports Mechanical Design: Useful for circular motion analysis in machinery and robotics.
Formula of Degrees ↔ Feet Calculator
The conversion between degrees and feet depends on the radius (r) of the circular path. The formulas used are:
1. Degrees to Feet Conversion
Feet = (Degrees / 360) × (2πr)
2. Feet to Degrees Conversion
Degrees = (Feet / (2πr)) × 360
Where:
- r = Radius (in feet)
- π ≈ 3.1416
- 360° represents a full circle.
These formulas help determine how much distance a certain degree of rotation covers along a circular arc.
Degrees ↔ Feet Reference Table
The table below provides pre-calculated values for common degrees and feet conversions based on different radii.
| Degrees | Radius (Feet) | Arc Length (Feet) |
|---|---|---|
| 1° | 100 | 1.75 |
| 5° | 100 | 8.73 |
| 10° | 100 | 17.45 |
| 15° | 100 | 26.18 |
| 30° | 100 | 52.36 |
| 45° | 100 | 78.54 |
| 60° | 100 | 104.72 |
| 90° | 100 | 157.08 |
| 180° | 100 | 314.16 |
| 360° | 100 | 628.32 |
This table provides a quick reference for estimating distances on circular paths.
Example of Degrees ↔ Feet Calculator
A road engineer needs to calculate the arc length for a 30° curve in a road with a radius of 200 feet.
Step 1: Apply the Formula
Feet = (30 / 360) × (2π × 200)
Step 2: Calculate the Arc Length
Feet = (30 / 360) × (2 × 3.1416 × 200)
Feet = (30 / 360) × (1256.64) = 104.72 feet
Thus, the arc length for a 30° curve with a 200-foot radius is approximately 104.72 feet.
Most Common FAQs
This conversion is crucial in road design, construction, and land surveying, where angular measurements need to be translated into real-world distances.
The radius depends on the circular path’s curvature, which is often predetermined in engineering and design applications.
Yes, astronomers use similar formulas to convert celestial arc distances into measurable surface distances on planetary bodies.