Calculate g-Force from Vertical and Horizontal Acceleration

Calculator for the resulting g-force from Earth's gravity and the acceleration on a horizontal plane. This is the force, which on Earth acts on an accelerating person or item. The gravity acceleration, which is pulling down, is 1 g. The perpendicular acceleration forward usually is lower.
Please enter two of the three values and choose the units, the third value will be calculated.

Gravity acceleration:		m/s²g
Horizontale acceleration:		m/s²g
g-force:		m/s²g

Round to 0 1 2 3 4 5 6 decimal places.

Example: when accelerating forward with 1 g, a force of 1.414 g is in effect. Since in this example both forces have equal values, the resulting force has the strength square root of two times one of the two initial forces, corresponding to the diagonal length in a square where the sides are of equal length.

The formula for the calculation is the Pythagorean theorem: g-force = √ gravity acceleration² + horizontale acceleration²

The Pythagorean theorem applies to a right triangle. Its legs are the two initial forces, and the resultant force is the hypotenuse. In the example above, the right triangle is also a diagonally bisected square.
In the case of horizontal motion on Earth, the two forces are perpendicular. But the movements can, of course, also be at a different angle to each other, for example, when moving uphill or downhill. In this case, adding forces is done using a force parallelogram.
The more both forces move in the same direction, i.e., the smaller the angle between them, the closer the resultant force is to the sum of both forces. If both forces work in opposite directions, i.e., at an angle of 180 degrees to each other, then the resultant force is the stronger minus the weaker initial force. The case discussed here, where both forces are perpendicular to each other, lies in the middle of these two extremes.

Last updated on 07/01/2025. Author: Jürgen Kummer


German: g-Beschleunigung