Calculate gyroscope angle, initial angle, angular velocity, or time from the other three values in degrees, radians, seconds, minutes, or hours.
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Gyroscope Angle Formula
The gyroscope angle calculation assumes constant angular velocity over the time interval. The main relationship is:
theta = theta_0 + omega*t
The same equation can be rearranged to solve for any missing value:
theta_0 = theta - omega*t
omega = (theta - theta_0)/t
t = (theta - theta_0)/omega
- theta = final angle
- theta_0 = initial angle
- omega = angular velocity
- t = time
The calculator lets you enter any 3 of the 4 values and solves for the missing one. It converts angles to degrees, angular velocity to degrees per second, and time to seconds before applying the formula. The result is then converted back to the unit you selected.
If you leave Angle blank, it calculates the final angle from the initial angle, angular velocity, and time. If you leave Initial Angle blank, it works backward from the final angle. If you leave Angular Velocity blank, it finds the rate of rotation. If you leave Time blank, it finds how long the rotation takes.
Angle, Rate, and Time Unit Conversions
These are the unit conversions used by the calculator before applying the gyroscope angle formula.
| Quantity | Unit | Conversion |
|---|---|---|
| Angle | Radians to degrees | 1 rad = 57.2958 degrees |
| Angle | Degrees to radians | 1 degree = 0.0174533 rad |
| Angular velocity | rad/s to deg/s | 1 rad/s = 57.2958 deg/s |
| Time | Minutes to seconds | 1 min = 60 s |
| Time | Hours to seconds | 1 hr = 3600 s |
Common Angle Values
| Degrees | Radians | Rotation Meaning |
|---|---|---|
| 90° | 1.5708 rad | Quarter turn |
| 180° | 3.1416 rad | Half turn |
| 360° | 6.2832 rad | Full turn |
| 720° | 12.5664 rad | Two full turns |
Example Problems
Example 1: Calculate the final angle
You have an initial angle of 20 degrees, an angular velocity of 15 degrees per second, and a time of 4 seconds.
theta = theta_0 + omega*t
theta = 20 + 15*4 = 80 degrees
The final angle is 80 degrees.
Example 2: Calculate angular velocity
You have a final angle of 200 degrees, an initial angle of 50 degrees, and a time of 10 seconds.
omega = (theta - theta_0)/t
omega = (200 - 50)/10 = 15 deg/s
The angular velocity is 15 degrees per second.
FAQ
What does a negative gyroscope angle mean?
A negative angle usually means the rotation is in the opposite direction from the positive direction you chose. For example, if clockwise is treated as positive, then counterclockwise rotation may appear as a negative angle.
Can this calculator use radians?
Yes. You can enter angle and initial angle in degrees or radians. You can also enter angular velocity in degrees per second or radians per second. The formula is the same, but the units must be consistent after conversion.
Why does time or angular velocity sometimes give an error?
Time cannot be zero when solving for angular velocity because the formula divides by time. Angular velocity cannot be zero when solving for time because the formula divides by angular velocity.