Enter the vertical rain speed (m/s) and the horizontal rain speed (m/s) into the Rain Angle Calculator. The calculator will evaluate the Rain Angle. 

Rain Angle Calculator

Enter any 2 values to calculate the missing variable

Rain Angle Formula

The rain angle describes the direction of the rain’s path when the drops have both a downward speed and a sideways speed caused by wind. This calculator treats the angle as being measured from the horizontal, so larger angles mean the rain is falling more steeply.

\theta = \tan^{-1}\left(\frac{V_y}{V_x}\right)
  • θ = rain angle
  • Vy = vertical rain speed
  • Vx = horizontal rain speed

This relationship comes from basic right-triangle trigonometry. The vertical rain speed forms one leg of the triangle, the horizontal rain speed forms the other leg, and the rain’s actual path is the diagonal velocity vector.

How to Calculate Rain Angle

  1. Determine the vertical rain speed.
  2. Determine the horizontal rain speed.
  3. Make sure both speeds use the same unit.
  4. Divide the vertical speed by the horizontal speed.
  5. Take the inverse tangent of that ratio.
  6. Report the answer in degrees or radians.

If the horizontal wind component increases while the vertical speed stays the same, the rain angle gets smaller and the rain appears more slanted. If the vertical speed increases while the horizontal speed stays the same, the angle gets larger and the rain falls more steeply.

Rearranged Forms

If you know the rain angle and one speed component, you can solve for the other unknown directly.

V_y = V_x \tan\left(\theta\right)
V_x = \frac{V_y}{\tan\left(\theta\right)}

These rearrangements are useful when you are estimating wind-driven rain, checking shelter exposure, or comparing how rainfall approaches a wall, window, vehicle, or overhang.

Angle Measured from the Vertical

Some people describe rain angle relative to the vertical instead of the horizontal. If that is the convention you need, use the complementary angle.

\theta_{vertical} = 90^\circ - \theta

That means a rain path of 59.04° from the horizontal is the same as 30.96° from the vertical.

Unit Conversion for Degrees and Radians

The inverse tangent function may return either degrees or radians depending on the calculator mode. These conversions are useful when switching between formats.

\theta_{deg} = \theta_{rad}\frac{180}{\pi}
\theta_{rad} = \theta_{deg}\frac{\pi}{180}

Example

Suppose the vertical rain speed is 5 m/s and the horizontal rain speed is 3 m/s.

\theta = \tan^{-1}\left(\frac{5}{3}\right) \approx 59.04^\circ
\theta \approx 1.03 \text{ rad}

This indicates the rain is falling at a fairly steep angle, but wind is still pushing it noticeably sideways.

Solving for a Missing Speed

If the rain angle is known, the calculator can also be used to find a missing speed component. For example, if the vertical speed is 6 m/s and the rain angle is 45°, then the horizontal speed is also 6 m/s.

V_x = \frac{6}{\tan\left(45^\circ\right)} = 6

Related Velocity Magnitude

Sometimes the direction alone is not enough, and you may also want the total speed of the rain along its path. That magnitude can be found with the Pythagorean relationship for the horizontal and vertical components.

V = \sqrt{V_x^2 + V_y^2}

Using the earlier example with 3 m/s horizontally and 5 m/s vertically, the rain’s total speed would be approximately 5.83 m/s.

Practical Interpretation

  • Near 90°: rain is falling almost straight down.
  • Around 45°: vertical and horizontal speeds are similar in size.
  • Near 0°: horizontal motion dominates and the rain path is very shallow.

Important Notes

  • Use consistent units for both speed inputs before applying the formula.
  • If the horizontal speed is zero, the rain falls straight down and the angle approaches 90° from the horizontal.
  • If the vertical speed is zero, the angle is 0°, representing purely horizontal motion.
  • If you only need the size of the angle, use speed magnitudes rather than signed velocity components.
  • This is a simplified 2D model and does not account for gusts, turbulence, or changing drop speed.