Ask Difference

Plane vs. Surface — What's the Difference?

By Maham Liaqat & Urooj Arif — Updated on April 22, 2024
Plane generally refers to a flat, two-dimensional surface extending infinitely in all directions, while a surface is any outer face or boundary of a solid object.
Plane vs. Surface — What's the Difference?

Difference Between Plane and Surface

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Key Differences

A plane is a fundamental concept in geometry, representing an idealized flat surface with no thickness and extending infinitely in all directions. It's defined by three non-collinear points or a point and a normal vector. On the other hand, a surface includes a wider variety of forms, including both flat and curved dimensions, which can be limited or extend indefinitely.
Planes are strictly two-dimensional, meaning they have length and width but no depth, making them ideal for mathematical and theoretical studies in fields like geometry and algebra. Surfaces, however, vary in dimensionality and can include shapes like spheres, cylinders, and more complex topologies in three-dimensional space.
In terms of application, planes are often used in mathematical proofs, architectural designs, and computer graphics to simplify calculations and representations. Whereas surfaces are crucial in more physically grounded applications like aerodynamics, industrial design, and topographical modeling.
Visualization of a plane is typically represented by a flat grid or sheet, emphasizing its uniformity and simplicity. In contrast, surfaces are visualized according to their nature; for example, a globe represents a spherical surface, illustrating the diversity and complexity possible with surfaces.
The concept of a plane is more abstract and theoretical, often serving as a building block for more complex mathematical concepts and theories. Surface, however, is a more tangible concept, directly applicable to physical objects and real-world scenarios, reflecting its practical importance across various scientific and engineering disciplines.
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Comparison Chart

Dimensions

Two-dimensional
Can be two- or three-dimensional

Curvature

Always flat
Can be flat or curved

Boundaries

Infinite (no edges or boundaries)
Can be finite or infinite

Defining Characteristics

Defined by three non-collinear points or a point and a normal vector
Defined by its geometry (e.g., planes, curves)

Applications

Used in mathematical theories, architecture
Used in practical applications like design, engineering

Compare with Definitions

Plane

Used in physics to describe hypothetical surfaces.
The mirror's reflection can be modeled as light interacting with a plane.

Surface

In computer modeling, a representation of an object's exterior.
The 3D model's surface was textured to add realism.

Plane

A flat, two-dimensional surface extending infinitely.
The artist drew a perfect straight line on the infinite plane.

Surface

The outermost layer of an object, which can be flat or curved.
The surface of the water was disturbed by the falling stone.

Plane

In architecture, a representation to visualize structures.
The architect used several planes to delineate the new building's layout.

Surface

In art, the canvas or material on which an artist works.
The painter applied a thick layer of paint across the canvas's surface.

Plane

A concept in geometry used to define linear equations.
The equation x + y = 1 defines a plane in a Cartesian coordinate system.

Surface

In physics, the interface between two phases.
Oil and water form a distinct surface at their boundary.

Plane

In computer graphics, a tool to simulate environments.
Video game developers use planes to create flat terrains.

Surface

In mathematics, a two- or three-dimensional boundary of a volume.
The sphere's surface is perfectly smooth.

Plane

(Mathematics) A surface containing all the straight lines that connect any two points on it.

Surface

A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space. It is the portion or region of the object that can first be perceived by an observer using the senses of sight and touch, and is the portion with which other materials first interact.

Plane

A flat or level surface.

Surface

The outside part or uppermost layer of something
Poor road surfaces
The earth's surface

Plane

A level of development, existence, or achievement
Scholarship on a high plane.

Surface

A continuous set of points that has length and breadth but no thickness.

Plane

An airplane or hydroplane.

Surface

Relating to or found on the surface of something
Surface layers

Plane

A supporting surface of an airplane; an airfoil or wing.

Surface

Rise or come up to the surface of the water or the ground
He surfaced from his dive

Plane

A carpenter's tool with an adjustable blade for smoothing and leveling wood.

Surface

Provide (something, especially a road) with a particular surface
A small path surfaced with terracotta tiles

Plane

A trowel-shaped tool for smoothing the surface of clay, sand, or plaster in a mold.

Surface

The outer or the topmost boundary of an object.

Plane

The plane tree.

Surface

A material layer constituting such a boundary.

Plane

(Mathematics) Of or being a figure lying in a plane
A plane curve.

Surface

The boundary of a three-dimensional figure.

Plane

Flat; level.

Surface

The two-dimensional locus of points located in three-dimensional space.

Plane

To smooth or finish with a plane
Planed the door.

Surface

A portion of space having length and breadth but no thickness.

Plane

To remove with a plane
Plane off the rough edges on a board.

Surface

The superficial or external aspect
"a flamboyant, powerful confidence man who lives entirely on the surface of experience" (Frank Conroy).

Plane

To work with a plane.

Surface

An airfoil.

Plane

To rise partly out of the water, as a hydroplane does at high speeds.

Surface

Relating to, on, or at a surface
Surface algae in the water.

Plane

To soar or glide.

Surface

Relating to or occurring on or near the surface of the earth.

Plane

To travel by airplane.

Surface

Superficial.

Plane

Of a surface: flat or level.

Surface

Apparent as opposed to real.

Plane

A level or flat surface.

Surface

To provide with a surface or apply a surface to
Surface a table with walnut.
Surface a road with asphalt.

Plane

(geometry) A flat surface extending infinitely in all directions (e.g. horizontal or vertical plane). Category:en:Surfaces

Surface

To bring to the surface
Surface a submarine.

Plane

(anatomy) An imaginary plane which divides the body into two portions.

Surface

To make known; expose or reveal
The first news report that surfaced the allegations.

Plane

A level of existence or development.
Astral plane

Surface

To rise to the surface.

Plane

A roughly flat, thin, often moveable structure used to create lateral force by the flow of air or water over its surface, found on aircraft, submarines, etc. (Compare airfoil, hydrofoil.)}}

Surface

To emerge after concealment.

Plane

Any of 17 designated ranges of 216 (65,536) sequential code points each.

Surface

To work or dig a mine at or near the surface of the ground.

Plane

A tool for smoothing wood by removing thin layers from the surface.

Surface

The overside or up-side of a flat object such as a table, or of a liquid.

Plane

An airplane; an aeroplane.

Surface

The outside hull of a tangible object.

Plane

(entomology) Any of various nymphalid butterflies, of various genera, having a slow gliding flight.

Surface

(figurative) Outward or external appearance.
On the surface, the spy looked like a typical businessman.

Plane

(entomology) The butterfly Bindahara phocides, family Lycaenidae, of Asia and Australasia.

Surface

The locus of an equation (especially one with exactly two degrees of freedom) in a more-than-two-dimensional space. Category:en:Surfaces

Plane

(countable) A deciduous tree of the genus Platanus.

Surface

(transitive) To provide something with a surface.

Plane

(Northern UK) A sycamore.

Surface

(transitive) To apply a surface to something.
The crew surfaced the road with bitumen.

Plane

To smooth (wood) with a plane.

Surface

(intransitive) To rise to the surface.
There was great relief when the missing diver finally surfaced.

Plane

To move in a way that lifts the bow out of the water.

Surface

(transitive) To bring to the surface.

Plane

To glide or soar.

Surface

To come out of hiding.

Plane

Any tree of the genus Platanus.

Surface

To become known or apparent; to appear or be found.

Plane

A surface, real or imaginary, in which, if any two points are taken, the straight line which joins them lies wholly in that surface; or a surface, any section of which by a like surface is a straight line; a surface without curvature.

Surface

(transitive) To make (information or facts) known.

Plane

An ideal surface, conceived as coinciding with, or containing, some designated astronomical line, circle, or other curve; as, the plane of an orbit; the plane of the ecliptic, or of the equator.

Surface

(intransitive) To work a mine near the surface.

Plane

A block or plate having a perfectly flat surface, used as a standard of flatness; a surface plate.

Surface

The exterior part of anything that has length and breadth; one of the limits that bound a solid, esp. the upper face; superficies; the outside; as, the surface of the earth; the surface of a diamond; the surface of the body.
The bright surface of this ethereous mold.

Plane

A tool for smoothing boards or other surfaces of wood, for forming moldings, etc. It consists of a smooth-soled stock, usually of wood, from the under side or face of which projects slightly the steel cutting edge of a chisel, called the iron, which inclines backward, with an apperture in front for the escape of shavings; as, the jack plane; the smoothing plane; the molding plane, etc.

Surface

Hence, outward or external appearance.
Vain and weak understandings, which penetrate no deeper than the surface.

Plane

Without elevations or depressions; even; level; flat; lying in, or constituting, a plane; as, a plane surface.

Surface

A magnitude that has length and breadth without thickness; superficies; as, a plane surface; a spherical surface.

Plane

To make smooth; to level; to pare off the inequalities of the surface of, as of a board or other piece of wood, by the use of a plane; as, to plane a plank.

Surface

That part of the side which is terminated by the flank prolonged, and the angle of the nearest bastion.

Plane

To efface or remove.
He planed away the names . . . written on his tables.

Surface

To give a surface to; especially, to cause to have a smooth or plain surface; to make smooth or plain.

Plane

Figuratively, to make plain or smooth.
What student came but that you planed her path.

Surface

To work over the surface or soil of, as ground, in hunting for gold.

Plane

Of a boat, to lift more or less out of the water while in motion, after the manner of a hydroplane; to hydroplane.

Surface

To rise from the depths of a liquid to the surface; as, the submarine surfaced to recharge its batteries.

Plane

An aircraft that has a fixed wing and is powered by propellers or jets;
The flight was delayed due to trouble with the airplane

Surface

To become known or public; - said of information.

Plane

(mathematics) an unbounded two-dimensional shape;
We will refer to the plane of the graph as the X-Y plane
Any line joining two points on a plane lies wholly on that plane

Surface

To show up, as a person who was in hiding; as, he absconded with the payroll and surfaced in Argentina.

Plane

A level of existence or development;
He lived on a worldly plane

Surface

The outer boundary of an artifact or a material layer constituting or resembling such a boundary;
There is a special cleaner for these surfaces
The cloth had a pattern of red dots on a white surface

Plane

A power tool for smoothing or shaping wood

Surface

The extended two-dimensional outer boundary of a three-dimensional object;
They skimmed over the surface of the water
A brush small enough to clean every dental surface
The sun has no distinct surface

Plane

A carpenter's hand tool with an adjustable blade for smoothing or shaping wood;
The cabinetmaker used a plane for the finish work

Surface

The outermost level of the land or sea;
Earthquakes originate far below the surface
Three quarters of the Earth's surface is covered by water

Plane

Cut or remove with or as if with a plane;
The machine shaved off fine layers from the piece of wood

Surface

A superficial aspect as opposed to the real nature of something;
It was not what it appeared to be on the surface

Plane

Travel on the surface of water

Surface

Information that has become public;
All the reports were out in the open
The facts had been brought to the surface

Plane

Make even or smooth, with or as with a carpenter's plane;
Plane the top of the door

Surface

A device that provides reactive force when in motion relative to the surrounding air; can lift or control a plane in flight

Plane

Having a horizontal surface in which no part is higher or lower than another;
A flat desk
Acres of level farmland
A plane surface

Surface

Come to the surface

Surface

Put a coat on; cover the surface of; furnish with a surface;
Coat the cake with chocolate

Surface

Appear or become visible; make a showing;
She turned up at the funeral
I hope the list key is going to surface again

Surface

On the surface;
Surface materials of the moon
Subsurface materials of the moon

Surface

Involving a surface only;
Her beauty is only skin-deep
Superficial bruising
A surface wound

Common Curiosities

How do planes differ from flat surfaces?

While all planes are flat surfaces, not all flat surfaces are planes; for example, a flat surface could have finite boundaries.

What types of surfaces are there?

Surfaces can be planar (flat), curved (like spheres or cylinders), or irregular, and can be either two- or three-dimensional.

What defines a plane in geometry?

A plane is defined by three non-collinear points or a point and a normal vector, extending infinitely without curvature.

How are planes used in computer graphics?

Planes are used in computer graphics to create environments and simulate horizons or flat terrains.

Can a surface be a plane?

Yes, a surface can be a plane if it is perfectly flat and extends infinitely.

What role do surfaces play in physics?

In physics, surfaces define interactions at boundaries, such as between different phases of matter.

How do mathematicians use the concept of surfaces?

Mathematicians study surfaces to understand complex geometries and topologies, crucial in fields like topology and differential geometry.

Are planes considered three-dimensional?

Planes are not considered three-dimensional; they are two-dimensional since they only have length and width.

What is the practical application of studying surfaces?

Studying surfaces is crucial in fields like material science, engineering, and art, where understanding the properties of surfaces can impact design and functionality.

Is there a difference in how planes and surfaces are visualized?

Yes, planes are generally visualized as flat grids, whereas surfaces might be depicted as curved or irregular shapes depending on their nature.

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Author Spotlight

Written by
Maham Liaqat
Co-written by
Urooj Arif
Urooj is a skilled content writer at Ask Difference, known for her exceptional ability to simplify complex topics into engaging and informative content. With a passion for research and a flair for clear, concise writing, she consistently delivers articles that resonate with our diverse audience.

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