Enter the vertical speed and ground speed into the calculator to determine the angle of climb.

Angle Of Climb Calculator

Enter any 2 values to calculate the missing variable

Related Calculators

Angle of Climb Formula

The following formula is used to calculate the angle of climb for a given vertical speed and ground speed.

\theta_{\deg}=\arctan\left(\frac{V_s}{G_s\cdot 101.27}\right)\cdot\frac{180}{\pi}

Variables:

  • (theta) is the angle of climb in degrees
  • (V_s) is the vertical speed in feet per minute
  • (G_s) is the ground speed in knots
  • 101.27 converts knots to feet per minute (1 knot ≈ 101.27 ft/min)

To calculate the angle of climb, convert the ground speed from knots to feet per minute by multiplying by 101.27, then divide the vertical speed by that value. Take the arctangent of the result to get the angle (in radians), and convert to degrees by multiplying by 180/π.

What is an Angle of Climb?

The angle of climb is the angle between the horizontal ground and the path of an aircraft as it ascends. It is an important parameter in aviation because it relates an aircraft’s vertical speed to its horizontal (ground) speed. The angle of climb is influenced by factors such as the aircraft’s speed, engine power, and aerodynamic properties. A steeper angle of climb (for a given ground speed) corresponds to a higher rate of climb, which can be crucial for avoiding obstacles and achieving optimal flight performance.

How to Calculate Angle of Climb?

The following steps outline how to calculate the Angle of Climb.

  1. First, determine the vertical speed ((V_s)) in feet per minute.
  2. Next, determine the ground speed ((G_s)) in knots.
  3. Next, calculate the angle of climb using the formula: θ(deg) = arctan( V_s / (G_s × 101.27) ) × (180/π).
  4. Finally, calculate the Angle of Climb.
  5. After inserting the values and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Vertical Speed ((V_s)) = 500 ft/min

Ground Speed ((G_s)) = 120 knots