Spheroidal Distance Calculator

✖Reduced distance is the distance which is reduced over the ellipsoid between the projections of the two points onto the ellipsoid.ⓘ Reduced Distance [K]			+10% -10%
✖Earth radius in km is the distance from the center of Earth to a point on or near its surface. Approximating earth as a spheroid, the radius ranges from 6,357 km to 6,378 km.ⓘ Earth Radius in km [R]			+10% -10%

✖Spheroidal distance is the shortest distance between two points on the surface of a sphere, measured along the surface of the sphere (as opposed to a straight line through the sphere's interior).ⓘ Spheroidal Distance [S]

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Spheroidal Distance Solution

STEP 0: Pre-Calculation Summary

Formula Used

Spheroidal Distance = Reduced Distance+((Reduced Distance^3)/(24*Earth Radius in km^2))
S = K+((K^3)/(24*R^2))
This formula uses 3 Variables

Variables Used

Spheroidal Distance - (Measured in Meter) - Spheroidal distance is the shortest distance between two points on the surface of a sphere, measured along the surface of the sphere (as opposed to a straight line through the sphere's interior).
Reduced Distance - (Measured in Meter) - Reduced distance is the distance which is reduced over the ellipsoid between the projections of the two points onto the ellipsoid.
Earth Radius in km - Earth radius in km is the distance from the center of Earth to a point on or near its surface. Approximating earth as a spheroid, the radius ranges from 6,357 km to 6,378 km.

STEP 1: Convert Input(s) to Base Unit

Reduced Distance: 49.5 Meter --> 49.5 Meter No Conversion Required
Earth Radius in km: 6370 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S = K+((K^3)/(24*R^2)) --> 49.5+((49.5^3)/(24*6370^2))

Evaluating ... ...

S = 49.5001245447687

STEP 3: Convert Result to Output's Unit

49.5001245447687 Meter --> No Conversion Required

FINAL ANSWER

49.5001245447687 ≈ 49.50012 Meter <-- Spheroidal Distance

(Calculation completed in 00.004 seconds)

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Created by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

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Meerut Institute of Engineering and Technology (MIET), Meerut

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Reduced Distance

LaTeX Go Reduced Distance = Earth Radius in km*sqrt(((Distance Traveled-(Elevation of b-Elevation of a))*(Distance Traveled+(Elevation of b-Elevation of a)))/((Earth Radius in km+Elevation of a)*(Earth Radius in km+Elevation of b)))

Spheroidal Distance for Tellurometers

LaTeX Go Spheroidal Distance = Reduced Distance+((Reduced Distance^3)/(43*Earth Radius in km^2))

Spheroidal Distance for Geodimeters

LaTeX Go Spheroidal Distance = Reduced Distance+((Reduced Distance^3)/(38*Earth Radius in km^2))

Spheroidal Distance

LaTeX Go Spheroidal Distance = Reduced Distance+((Reduced Distance^3)/(24*Earth Radius in km^2))

Spheroidal Distance Formula

LaTeX Go

Spheroidal Distance = Reduced Distance+((Reduced Distance^3)/(24*Earth Radius in km^2))
S = K+((K^3)/(24*R^2))

What is Horizontal Distance and Angles in Surveying and How is it measured?

A linear measurement on the horizontal plane determines the horizontal distance between two points. However, the true horizontal distance is actually curved like the Earth’s surface. Due to this curvature, the direction of gravity is different at each point.

Horizontal angles are measured on the horizontal plane and establish the azimuth of each survey measurement. An azimuth is a horizontal angle measured clockwise from a defined reference (typically geodetic north).

How to Calculate Spheroidal Distance?

Spheroidal Distance calculator uses Spheroidal Distance = Reduced Distance+((Reduced Distance^3)/(24*Earth Radius in km^2)) to calculate the Spheroidal Distance, The Spheroidal Distance formula is defined as the shortest distance between two points on the surface of a sphere, measured along the surface of the sphere (as opposed to a straight line through the sphere's interior). Spheroidal Distance is denoted by S symbol.

How to calculate Spheroidal Distance using this online calculator? To use this online calculator for Spheroidal Distance, enter Reduced Distance (K) & Earth Radius in km (R) and hit the calculate button. Here is how the Spheroidal Distance calculation can be explained with given input values -> 49.50012 = 49.5+((49.5^3)/(24*6370^2)).

FAQ

What is Spheroidal Distance?

The Spheroidal Distance formula is defined as the shortest distance between two points on the surface of a sphere, measured along the surface of the sphere (as opposed to a straight line through the sphere's interior) and is represented as S = K+((K^3)/(24*R^2)) or Spheroidal Distance = Reduced Distance+((Reduced Distance^3)/(24*Earth Radius in km^2)). Reduced distance is the distance which is reduced over the ellipsoid between the projections of the two points onto the ellipsoid & Earth radius in km is the distance from the center of Earth to a point on or near its surface. Approximating earth as a spheroid, the radius ranges from 6,357 km to 6,378 km.

How to calculate Spheroidal Distance?

The Spheroidal Distance formula is defined as the shortest distance between two points on the surface of a sphere, measured along the surface of the sphere (as opposed to a straight line through the sphere's interior) is calculated using Spheroidal Distance = Reduced Distance+((Reduced Distance^3)/(24*Earth Radius in km^2)). To calculate Spheroidal Distance, you need Reduced Distance (K) & Earth Radius in km (R). With our tool, you need to enter the respective value for Reduced Distance & Earth Radius in km and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Spheroidal Distance?

In this formula, Spheroidal Distance uses Reduced Distance & Earth Radius in km. We can use 2 other way(s) to calculate the same, which is/are as follows -

Spheroidal Distance = Reduced Distance+((Reduced Distance^3)/(43*Earth Radius in km^2))
Spheroidal Distance = Reduced Distance+((Reduced Distance^3)/(38*Earth Radius in km^2))

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