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This conversion calculates the linear distance (in inches or feet) that corresponds to a given angle (in degrees) on a circle with a specific circumference. It's useful in engineering, construction, and mechanical applications where rotational motion needs to be converted to linear distance.
The calculator uses these formulas:
Where:
Explanation: The formula works by calculating what fraction of the full circle's circumference corresponds to the given angle (degrees/360).
Details: This calculation is essential in scenarios like determining how much cable will be wound/unwound from a spool when rotated a certain amount, calculating linear movement from rotary encoders, or designing mechanical systems with rotational components.
Tips: Enter the angle in degrees and the circumference in inches. Both values must be positive numbers. The calculator will provide both inch and foot measurements for convenience.
Q1: Why divide by 360 in the formula?
A: There are 360 degrees in a full circle, so dividing by 360 gives the fraction of the circumference that corresponds to the given angle.
Q2: Can I use this for metric measurements?
A: The calculator works with inches and feet. For metric, you could enter circumference in centimeters and then convert the result from inches to centimeters if needed.
Q3: What if I know the diameter instead of circumference?
A: First calculate circumference using \( Circumference = \pi \times Diameter \), then use that value in the calculator.
Q4: Does this work for any size circle?
A: Yes, as long as you know the circumference, the formula works for circles of any size.
Q5: How accurate is this calculation?
A: The calculation is mathematically precise. Any inaccuracy would come from measurement errors in the degrees or circumference values.