The words 'plane' and 'plain' have several meanings. Unfortunately, both have a meaning relating to flatness, and this is
often the source of confusion.
Plain
The word plain has several meanings:
Simple (i.e., not
elaborate).
a
plain girl 
a
plain cake 
a
plain colour 
Also simple as in apparent.
It is
plain to see. 
It
seems quite plain to me. 
Plain is an adjective in these
examples. |
An expanse of level
and low land.
The
Russian Plain. 
I
joined the Chinese farmers as they attempted to drive the yaks across the
plain in western China. 
Plain is a noun in these examples.
|
Plane
The word plane has several meanings:
An airplane.
What
time is your plane?
|
A flat surface
(especially in mathematics) .
In a
3D space, a plane can be defined by specifying a point and a normal vector to the plane.

Also means a level (usually figurative).
I was
hoping for a conversion on a higher plane.  |
A tool for smoothing or shaping wood
(i.e., a carpenter's plane).
Also the verb 'to plane' (i.e., to shape wood).
Can
you plane a few inches off the top of the door?  |
To travel on the
surface of water.
The
car hit the puddle and planed straight into the back of the lorry. 
(also known as 'to aquaplane') |
Select the correct version:
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Confusion arises mostly between 'plain' meaning expanse of lowland and 'plane'
meaning a flat surface or a level.
A plain (lowland) is always on the ground; whereas, a plane (a surface or a
level) is nearly always above the ground...like an airplane.
Therefore, if it's above the ground, it's almost certainly 'plane'.
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