Units Dimensions and Conversions

Area measures the size of a surface using length measurements in two dimensions. An area is being measured if two length units are multiplied such as square inch or square centimeter, or if a special area unit such as acre or hectare is used.

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Density

Density measures how much of a substance is contained in a given volume. Stating this more carefully gives a math clue for determining density's units: Density is the mass per unit volume of a substance. So the units for density are mass units divided by volume units.

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Acceleration

Acceleration is a measure of how fast velocity is changing, so we can think of it as the change in velocity over time. This gives the units clue: velocity over time.

The most common use of acceleration is acceleration due to gravity which can also appear as the gravitational constant (you might have seen it as .)

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Volume

Volume measures the size of an object (not just the surface) using length measurements in three dimensions. A volume is being measured if three length units are multiplied, such as cubic inch or cubic centimeter, or if a special volume unit such as fluid ounce or liter is used.

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Velocity

Velocity gives an indication of the speed of an object by measuring the change in position (measured as a length) over time. This gives the crucial clue to the units: distance over time.

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Force

A force is an entity that when applied to a mass causes it to accelerate. Sir Isaac Newton's Second Law of motion states that

the magnitude of a force = mass * acceleration.

This gives the units clue: mass * acceleration.

This combination of units has been given the name Newton (N) in honor of Sir Isaac. The most common use of force is force of an object due to gravity (we call it weight!) which is calculated using mass * gravitational acceleration.

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The Shodor Education Foundation, Inc.
in cooperation with the Department of Chemistry,
Appalachian State University