Every road gradient, every drainage scheme and every building foundation depends on knowing how high things are. Levelling is the operation that determines it — and it rests on a surprisingly subtle idea, because “height” has to be measured from somewhere, and the surface of the earth is curved.
What Levelling Is
Levelling is the operation required in the determination — or more strictly, the comparison — of heights of points on the surface of the earth.
Why “Comparison” Is the Better Word
The correction in that definition matters. A level does not measure absolute height; it measures the difference between two points.
This is the same idea as the surveying definition itself, which speaks of the relative positions of features. Levelling extends that principle into the vertical dimension — everything is referred to something else, and absolute heights only emerge once a reference is chosen.
The Datum
If a whole series of heights is given relative to a plane, this plane is called a datum. In topographical work the datum used is the mean level of the sea, because it makes international comparison of heights possible.
Why Mean Sea Level
The reason given is worth appreciating. Any plane could serve as a datum — the floor of a building, an arbitrary level, anything. But a purely local datum makes heights meaningless outside that survey.
The sea, by contrast, is shared by every country. Adopting mean sea level means a height measured in India can be compared directly with one measured anywhere else. It is a datum chosen for universality, not convenience.
How Mean Sea Level Is Determined
The value for mean sea level as datum is obtained by averaging the elevations of high and low tides, at several points, for a long period of time — about 19 years.
Why 19 Years
This figure looks oddly specific, and it is. Tides are driven by the moon as well as the sun, and the moon’s orbital plane itself rotates on a cycle of roughly 18.6 years.
Averaging over a shorter period would capture only part of that cycle and leave a bias in the result. Averaging over about 19 years covers a complete cycle, so every tidal condition is represented in proportion and the mean is genuinely stable.
Note also “at several points” — a single tide gauge could be affected by local conditions of coastline and currents, so multiple stations are used.
Levels
The vertical heights of points above or below a datum are referred to as levels.
Level Line and Horizontal Line
This distinction is the most important idea in the topic, and it is where levelling meets the curvature of the earth.
Level Line
A level line is one that is at a constant height relative to mean sea level, and because it follows the mean surface of the earth it must be a curved line.
Horizontal Line
A horizontal line is tangential to the level line at any particular point, because it is perpendicular to the direction of gravity at that point.
The Two Compared
| Level Line | Horizontal Line | |
|---|---|---|
| Shape | Curved | Straight |
| Height above MSL | Constant everywhere along it | Constant only at the point of tangency |
| Defined by | Following the mean surface of the earth | Being perpendicular to gravity at a point |
| Relationship | — | Tangential to the level line |
Why This Matters
For short distances these two lines are considered to coincide with each other; but for long distances a correction for their divergence becomes necessary.
Here is the crux of the problem. A levelling instrument, once its bubble is centred, gives a horizontal line of sight — because the bubble responds to gravity at that one point. But the surface of constant height is a level line, which curves away downwards.
The further you sight, the more the straight horizontal line rises above the curved level line — and the staff reading is affected accordingly.
The Consequence Made Concrete
Although points A and B may both be at mean sea level, due to the curvature of the level line it will be misconstrued that point B is below mean sea level. Thus it is clear why a correction is required for the effect of curvature.
Two points genuinely at the same height appear to differ, purely because the instrument’s line of sight is straight while the surface of equal height is curved. This is not an instrument fault — it is geometry, and it is why the curvature and refraction corrections exist.
Note how closely this parallels the plane-versus-geodetic surveying problem. There, a flat horizontal plane departed from the curved earth over large areas. Here, a straight horizontal line departs from the curved level line over long sights. Same curvature, same consequence, different dimension.
How a Level Actually Measures Height
The difference in the readings on a vertically held graduated staff, where it is intersected by the horizontal line of sight, is a direct measure of the difference in height between the two staff stations.
The Simplicity of the Method
This deserves a moment’s thought, because it explains why levelling is so reliable.
The instrument establishes one horizontal line of sight. A staff held at point A is intersected at some reading; a staff at point B is intersected at another. Both readings are measured downwards from the same horizontal line.
So the difference between the readings is the difference in height. No trigonometry, no distance measurement, no calculation — just subtraction.
Note also the direction of the relationship: a higher staff reading means a lower point, because the staff has to extend further up to reach the line of sight. This is exactly the rule used in the rise and fall method of booking.
Elevation and Altitude
| Term | Definition |
|---|---|
| Elevation | The vertical distance of a point above or below the datum surface |
| Altitude | The vertical distance of a point above mean sea level |
It should be noted that vertical distances are measured along the direction of gravity.
Therefore, if the datum surface is mean sea level, the elevation is the same as the altitude.
The Distinction in One Sentence
Elevation is measured from whatever datum you chose; altitude is measured specifically from mean sea level.
They coincide only when the chosen datum is mean sea level — which in topographical work it usually is, which is why the two words are often used interchangeably. But if a site survey uses an arbitrary datum, the elevations recorded are not altitudes.
Note too that vertical distance is defined by gravity, not by geometry — the same physical definition used for the horizontal plane in the fundamentals chapter.
Vertical Line
A vertical line is a line from any point on the earth’s surface to the centre of the earth. It is commonly considered to be the line defined by a plumb line.
The two halves of this definition agree because gravity pulls towards the earth’s centre, so a freely hanging plumb line naturally aligns itself along that direction. The plumb bob is simply gravity made visible.
This also explains why vertical lines at different places are not parallel — they all converge on the earth’s centre, just as true meridians converge on the poles.
Quick Revision Notes
- Levelling determines, or more strictly compares, the heights of points on the earth’s surface.
- A datum is the plane relative to which heights are given; in topographical work it is mean sea level, because it allows international comparison.
- MSL is obtained by averaging high and low tides at several points for about 19 years.
- Vertical heights above or below a datum are called levels.
- A level line is curved — at constant height relative to MSL, following the mean surface of the earth.
- A horizontal line is straight — tangential to the level line, perpendicular to gravity at that point.
- The two coincide over short distances; over long distances a correction for divergence is needed.
- The difference in staff readings is a direct measure of the difference in height.
- Elevation is measured from the datum; altitude is measured from mean sea level. They are equal when the datum is MSL.
- Vertical distances are measured along the direction of gravity.
- A vertical line runs from a point to the centre of the earth and is defined by a plumb line.
Mistakes Students Commonly Make
- Confusing level line and horizontal line. The level line is curved; the horizontal line is straight and tangential to it.
- Saying a level line is straight because water is level. Water follows the earth’s curvature, so a level line must be curved.
- Treating elevation and altitude as always identical. They agree only when the datum is mean sea level.
- Giving the MSL averaging period as 9 or 10 years. It is about 19 years.
- Forgetting that a higher staff reading means a lower point.
- Defining a horizontal line geometrically. It is defined by being perpendicular to gravity.
- Saying vertical lines are parallel. They converge at the earth’s centre.
Conclusion
Levelling compares heights, and everything in it follows from one geometric fact — the surface of constant height is curved, while the line of sight a bubble gives you is straight. Over a short sight the difference is negligible and the two can be treated as one; over a long sight it must be corrected, or points genuinely at sea level will appear to sink below it. Mean sea level serves as the datum because the sea belongs to everyone, averaged over about 19 years so that the full lunar tidal cycle is captured.
Frequently Asked Questions
What is levelling?
The operation required in the determination, or more strictly the comparison, of heights of points on the surface of the earth.
What is a datum?
The plane relative to which a series of heights is given. In topographical work the datum used is the mean level of the sea.
Why is mean sea level used as the datum?
Because it makes international comparison of heights possible, being a reference shared by every country rather than a purely local one.
How is mean sea level determined?
By averaging the elevations of high and low tides at several points over a long period of about 19 years.
Why is the averaging period about 19 years?
Because the moon’s orbital plane rotates on a cycle of roughly 18.6 years, so averaging over about 19 years covers a complete tidal cycle and removes bias from the result.
What is the difference between a level line and a horizontal line?
A level line is at constant height relative to mean sea level and is curved, since it follows the mean surface of the earth. A horizontal line is straight and tangential to the level line, being perpendicular to the direction of gravity at that point.
Why is a correction for curvature necessary?
Because a levelling instrument gives a straight horizontal line of sight while the surface of constant height curves away from it. Over long sights, two points genuinely at the same level would appear to differ in height.
How does a level measure the difference in height?
The difference in the readings on a vertically held graduated staff, where it is intersected by the horizontal line of sight, is a direct measure of the difference in height between the two staff stations.
What is the difference between elevation and altitude?
Elevation is the vertical distance of a point above or below the chosen datum surface, while altitude is the vertical distance above mean sea level. If the datum is mean sea level, the two are the same.
What is a vertical line?
A line from any point on the earth’s surface to the centre of the earth, commonly considered to be the line defined by a plumb line.