Tuesday, 27 Sep 2022
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Dimensional Analysis Calculator | Definition, Unit Converter & Examples

The Dimensional Analysis Calculator is a free online application that may be used to calculate the dimensions of two physical quantities. Dimensional analysis is the study of the relationships between different physical quantities by identifying their base quantities (like length, mass, time, and electric current) and units of measure (like miles vs. kilometers, or pounds vs. kilograms) and tracking these dimensions as calculations or comparisons are performed in engineering and science. Converting units from one dimension to another in the metric or SI system is often easier than in other systems because all units utilize the same 10-base.

However, for such conversions involving algebraic principles, the factor-label approach, also known as the unit-factor method, is a popular way. However, by assessing the two physical characteristics in a matter of seconds, our online dimensional analysis calculator application speeds up the procedure.

Dimensional Analysis Calculator with Steps

The Dimensional Analysis calculator can be used as follows:

  • Step 1:

In the Dimensional analysis calculator, first fill in the appropriate input areas with two physical quantities.

  • Step 2:

After that, click the “Submit” button to get the analysis.

  • Step 3:

Finally, our dimensional analysis calculator will display the dimensional analysis in a new window.

Dimensional Analysis Definition

It could be easier to work with if a mass in grams was expressed in milligrams (10–3 g). The process of converting between metric units is known as unit analysis, sometimes known as dimensional analysis.

Unit analysis, on the other hand, is a proportional reasoning process in which a given measurement is multiplied by a known percentage or ratio to obtain a result with a new unit or dimension. However, any integer multiplied by one remains the same, as we know from algebra. When we multiply a number with units by a ratio with units, the number’s units multiply and divide by the ratio’s units, returning the original value (remember, you’re multiplying by one), but with different units.

However, by multiplying or dividing a given integer by a known ratio, this procedure can be generalized to obtain your answer. The supplied number is a number having a numerical value (with its units). The ratio’s denominator units correspond to the numerator units of the provided, while the numerator units correspond to either the next ratio or the ultimate answer. You’ll get the correct units for your solution if you multiply these together.

Dimensional Analysis Calculator Moles

The number of moles in a substance of a particular mass is calculated using a dimensional analysis calculator. This gram to mole converter, on the other hand, will instantly show you how to convert moles to grams for any chemical. It can, however, be used to convert grams to moles in the other direction. Meanwhile, keep reading to learn the formula for converting grams to moles, try solving a problem involving how to convert grams to moles on your own, and never worry about converting g to mol again.

Dimensional Analysis Calculator Practice

When working on dimensional analysis problems, follow these steps:

  • Recognize the situation (see the previous concept for additional information).
  • Then figure out the conversion factors that will help you get from your current units to the one you want.
  • Make your equation such that the undesirable units are cancelled out, leaving only the desired units. It cancels out when a unit appears in both the numerator and the denominator of an equation.
  • Multiply all of the numbers together to get the final result. Remember to include the units and sig figs in your calculations.

Dimensional Analysis Calculator Volume

Meanwhile, you can use this metric dimensional analysis calculator to convert: cubic metres to cubic feet gallons to litres cubic feet to gallons

Convert cubic feet to litres, cubic metres to cubic feet, cubic inches to cubic feet, and litres to cubic feet after that.

Convert units between the metric systems of the United States and the United Kingdom, as well as the standard metric system (SI).

The volumes of various geometrical bodies, on the other hand, can be determined. A pyramid, a truncated pyramid, a cylinder, a hollow cylinder (pipe), a cone, a truncated cone, a sphere, a sphere segment, and a barrel are all examples of these. You’ll need to make sure the units are all the same. As a result, you’ll need to provide all of the data in metres if you want the volume in cubic metres. If you don’t, your calculations will be inaccurate.

Dimensional Analysis Calculator

Dimensional Analysis Calculator Time

The quickest way to convert seconds to hours is to use the following formula:

seconds = 3,600 hours

Multiplying the time in seconds by 3,600 yields the time in hours. Because there are 3,600 seconds in an hour, the conversion ratio used in the formula is 3,600 seconds per hour.

You can convert 5,400 seconds to hours, for example, using the method shown above.

5,400 sec = (5,400 ÷ 3,600) = 1.5hour

The formula above can be used to calculate the hours in decimal form, but these procedures can also be used to calculate the hours, minutes, and seconds.

  • Multiply the seconds by 3,600 to get the total hours. Then use the number to the left of the decimal point as the number of hours.
  • The remaining seconds are calculated by multiplying the even hours above by 3,600. Subtract that from the total number of seconds in the meantime.
  • Divide the remaining seconds by 60 to get the total number of minutes. Then use the number to the left of the decimal point as the number of minutes.
  • To get the remaining seconds, multiply the even minutes found above by 60. Take that number and subtract it from the total number of seconds. In a nutshell, this is the number of seconds left.
  • Fill in the HH: MM: SS form with the even number of hours, minutes, and seconds remaining.

Dimensional Analysis Calculator with sig figs

Physical quantities, on the other hand, require the use of a unit to express their value. How else would we tell the merchant how much sugar, bread, oil, and other supplies we’ll need? On the other hand, the number of physical quantities we measure is huge. Consider how difficult it would be to remember all of them if each was assigned its own unit.

Most physical quantities, on the other hand, can be stated with a small number of units. “Basic units” or “fundamental units” are the terms used to describe these. Meanwhile, the physical quantities represented by these fundamental units are the seven dimensions of the physical world.

The seven physical quantities are listed below, together with their base units (in SI) and dimensions:

  • Length: m (meter) [L]
  • Then, Mass: kg (kilogram) [M]
  • Time: s (second) [T]
  • Then, Electric current: A (Ampere) [I]
  • Temperature: K (Kelvin) [Θ]
  • Then, the Amount of substance: mol (mole) [N]
  • Then, Luminous intensity: cd (candela) [J].

These fundamental units can also be used to represent other quantities. For example, the area is calculated as a product of the side lengths, therefore we can express it in m2 units and dimensions of [L2]. Units that can be expressed in terms of basic units are referred to as derived units.

The units listed below are some of the most typically derived units:

  • Area: m²
  • Then, Volume: m³
  • Velocity: m/s
  • Then, Acceleration: m/s²
  • Density: g/mL or g/cm³
  • Then, Force: kg× m/s², or the Newton (N)
  • Then, Energy: N×m, or the Joule (J)

How to use the dimensional analysis calculator to solve dimensional analysis problems?

Let’s look at how we can convert the value of g (gravitational acceleration) from m/s2 to km/h2 using the dimensional analysis calculator (or unit analysis calculator).

Select the choice to convert units from the drop-down menu.

Choose between base and derived units from the drop-down menu. Select “Derived units” for this example.

Under the physical quantity section, choose acceleration.

Enter the physical quantity’s value and unit, for example, 9.8 and m/s2.

Choose your desired unit in the unit conversion area, such as km/h2.

The unit analysis calculator will convert 9.8 m/s2 to 127,008 km/h2 using the value of g.

The dimensional analysis calculator can also be used to compare the dimensions of two measures. We propose that you double-check that the radius of the Earth (6378 km) is 1.8759 * 108 times that of a tennis ball (3.4 cm).

Dimensional Analysis Calculator unit Converter

Derived quantity Symbol SI derived unit Dimension
Abasement A m⋅s L T
Similarly, the Absorbed dose rate Also, Gy/s Similarly, L² T^−3
Then, Acceleration

a

m/s² Similarly, L T^−2
Similarly, Angular acceleration ωa Also, rad/s² T^-2
Then, Angular momentum L kg⋅m²/s Similarly, M L² T^-1
Similarly, Angular velocity ω Also, rad/s Similarly, T^-1
Then, Area A m2
Similarly, Area density ρA Also, kg⋅m^−2 Similarly, M L^-2
Then, Capacitance C farad (F = C/V) Similarly, M^-1 L^-2 T⁴ I²
Similarly, Catalytic activity concentration Also, kat⋅m^−3 L^-3 T^-1 N
Then, Centrifugal force Fc N⋅rad = kg⋅m⋅rad⋅s^−2 Similarly, M L T^−2
Similarly, Chemical potential μ Also, J/mol L T^−5
Then, Crackle

C

m/s^5 Similarly, L^−2 I
Similarly, the Current density

J

Also, A/m² Similarly, L² T^−2
Then, the Dose equivalent H sievert (Sv = m²/s²) M L^−1 T^−1
Similarly, Dynamic viscosity v Also, Pa⋅s Similarly, T I
Then, Electric charge Q coulomb (C = A⋅s) Similarly, L^−3 T I
Similarly,

, Electric charge density

ρQ Also, C/m³ L^−2 T I
Then, the electric displacement field

D

V/m Similarly, M L T^−3 I^−1

Dimensional Analysis Calculator in Chemistry

Dimensional analysis is used by chemists and other professionals to convert units of measurement. Any unit of the same dimension can be converted to another of the same dimension. This means we may translate a specific number of seconds into another time unit, such as minutes, because one minute always contains 60 seconds. Alternatively, knowing that one kilogram is always 1000 grams, we can convert a given mass in grams to kilograms. Although metric units are most typically used in chemistry, we may also convert lengths from kilometres to miles. However, using a known conversion factor, it is sometimes possible to convert to a new dimension. One litre is equal to one kilogram of clean water, for example. You could, however, use that information to convert a volume of water to a mass of water or vice versa.

Read Also: How to write an equation in slope intercept form?

Meanwhile, in chemistry, time, mass, length, and volume are some of the most regularly used dimensions. The International System of Units (SI units) are the standard units of measurement (those used most commonly so that they may be easily communicated with other scientists). The SI unit of time, however, is seconds, which is represented by the letter s. The SI unit of mass is the kilogram. It’s written as kg, with the k denoting kilo and the g denoting gram, the fundamental unit of mass. The SI unit of length is the metre (symbol m). Chemists also use moles to measure the amount of a chemical, which is a SI unit. A mole, on the other hand, is made up of about 6.022 x 1023 particles (atoms or molecules). Mol is the symbol for it.

Dimensional Analysis in Physics

When working on physics problems, you’ll frequently be asked to determine the numerical value and units of a variable in an equation. For a beginner, the numerical value is usually not difficult to obtain, but the same cannot be said for the units. Dimensional analysis, on the other hand, is a useful method for determining the units of a variable in an equation, and it is covered in this self-instruction topic.

The bulk of physical quantities, on the other hand, may be expressed in terms of five basic dimensions. The Greek letter theta () however, stands for mass (M), length (L), time (T), electrical current (I), and temperature (T) (T). Because they are easy to quantify in studies, these five dimensions were chosen as the foundation. Dimensions and units are not the same thing.

Dimensional Analysis Calculator

Dimensional Analysis Calculator Medication

The dimensional analysis calculator method uses a set of equivalency conversion factors to convert one measurement system to another without the need to memorise specific formulas. This method reduces errors and can be applied to any dosage calculation.

  • Begin by deciding on the label or unit of measurement that will be used in the response.
  • Then, in the numerator, enter data with the same label as the previous denominator to complete the equation. Any unwanted labels will be removed as a result of this. Continue until you’ve cancelled out all of the units of measure that aren’t needed in the answer.
  • Calculate the numeric answer that is labelled correctly. Before rounding any numbers in the equation, wait until you get the final solution.

Example

IV Dose of any drug:

Once a day, digoxin 0.5 mg IV should be given. The pharmaceutical concentration available from the pharmacist is Digoxin 0.25 mg/mL. How much mL will you need to give a 0.5 mg dose?

  • The first step is to:

To begin, what type of measurement unit (label) is required? But this is on the left side of the equation.

mL?, =

  • 2nd step:

Then, on the right side of the page, write the information with the same label as the numerator. In this example, we know that the medicine concentration available is 0.25 mg/mL. Meanwhile, write mL in the numerator and 0.25 mg in the denominator.

mL? = mL/0.25mg

  • 3rd step:

The suggested dosage, however, is 0.5 mg. Meanwhile, enter information into the numerator equation with the same label as the preceding denominator to cancel out the unwanted labels. Rep this process until you’ve removed all of the unwanted labels.

mL? = (mL/0.25mg) × 0.5mg =

  • 4th step:

Multiply the numerator by the denominator, then the denominator by the numerator. Meanwhile, divide the numerator by the denominator to reach the final solution with the correct label.

mL?  = (mL/0.25mg) × 0.5mg = 0.5mL/0.25 = 2mL

 Final answer: Suggest 2 mL of digoxin daily.

Dimensional Analysis to Remember Equation

For example, the physical amount of speed could be measured in metres per second, miles per hour, or other units. We refer to the dimensions of speed as length divided by time, or simply L/T, because speed is always a length divided by time, regardless of the units used. Similarly, the area’s dimensions are L2 because the area can always be computed as a length. The area of a circle is generally written as r2, but it may also be written as

πr (which is a length) × r (another length).

Assume you’re unsure if time = distance/speed or time equals distance/speed.

However, we can double-check this by making sure all sides of the equations have the same dimensions.

By reducing both equations to their fundamental units on each side of the equation, we get

[T] = [ LT^(-1) / L ] = [T^(-1)]    (Wrong)

[T] = [ L / LT^(-1) ] = [T¹]    (Right)

Dimensional Analysis Examples

Example 1

If you have a sample of a substance with a mass of 0.0034 grams and want to express it in mg, you can use the dimensional analysis below. The supplied quantity, however, is 0.0034 grams of mass. Meanwhile, the quantity you’re seeking for is the mass in mg, and we know that 1 mg = 10-3 g. The proportion or ratio is one milligram per tenth of a gram, or 1000 mg/1 gram.

As a result, 0.0034g x (1 gram/1 gram) = 3.4 mg

Example 2

How many hours are in 3 days?

Ans.

  • Recognize these facts: three working days
  • Calculate the following conversion factors to help you go from your original units to the unit you want:

24 hours/ 1day

  • Set up the equation so that the undesirable units cancel out and the required units remain:
  • 3 days (1 day = 24 hours)
  • Multiply the equation to get your final answer. The final response time is 72 hours.

Example 3

How many inches are in 5 feet?

Ans.

  • The given measurement is 5 feet.
  • 12 inches / 1 foot is the conversion factor.
  • Create the following equation:

5 feet × 12 inches (1 foot)

  • Multiplying by: 60 inches in length

How many feet does 30 inches equal?

Ans.

30 inches × ( 1 feet / 12 inches ) = 2.5feet

Dimensional analysis calculator application

We can use Dimensional analysis to solve problems in physics, engineering, mathematics, medicine, and chemistry. We also use dimensional analysis in a variety of ways, including:

  • Converting one system of units to another — You may do this with our dimensional analysis calculator.
  • Examining the formula for correctness – We may determine whether a particular formula is valid or not by checking the equations for dimensional consistency. Consider the following equation for uniform motion: s = v * t.

Here, s denotes the displacement, which has length [L], velocity [L T-1], and time [T] dimensions. L T-1 * T = L L.H.S = R.H.S

As a result, the equation is dimensionally valid and consistent.

  • Formula derivation – We can also deduce a physical quantity’s formula by testing for dimensional consistency.

Some Frequently Asked Questions about Dimensional Analysis Calculator

What is dimensional analysis?

When there isn’t enough data to create precise equations, a method of analysis in which we characterize physical quantities in terms of their fundamental dimensions that we commonly use.

What is the principle of Homogeneity of dimension?

Each term in a dimensional equation has the same dimensions on both sides, according to the concept of homogeneity.

How many kilograms go into a gram?

1 gram (g) equals 0.001 kilograms (kg).

What exactly is a dimensional analysis, and why is it useful?

We reduce physical quantities such as acceleration, viscosity, and energy to their basic dimensions of length (L), mass (M), and time (T) using dimensional analysis (T).

How do you calculate dimensions?

To achieve a three-dimensional measurement, measure all three properties of an object: length, width, and height. Continuing with the previous example, the 3 ft. x 4 ft. rectangle is the side of a box with a length of 5 feet, thus the measurements are 3 ft. (width) x 4 ft. (height) x 5 ft.

What is a dimensional formula?

The dimensional formula is the statement of a physical quantity in terms of its fundamental unit with suitable dimensions. Dimensional force is an example. [M L T-2] F = [M L T-2] The reason for this is that the unit of Force is Newton, or kg*m/s2. Equation with three dimensions.

How do you convert between units?

To convert a smaller unit to a larger unit (for example, to), multiply it by the number of smaller units required to make the larger unit. Multiply to convert from a larger to a smaller unit. Divide to convert from a smaller to a larger unit.

How do you find the dimension of an area?

We measure the length of a shape’s outline by its perimeter. We also measure perimeter in feet, inches, or millimetres. However, we measure the area in square units. Use the following formula to calculate area: L multiplied by W equals area.