The dimensional analysis calculator is a tool that allows you to calculate the dimension of an equation or relationship between physical quantities. Dimensional analysis is an important technique in physics and engineering to check the consistency of equations and identify possible errors or omissions.
Dimensional analysis is based on the fact that physical quantities can be expressed as products of base units. For example, force can be expressed as the product of mass, acceleration, and time: F = mThet. The force dimension is therefore the mass dimension multiplied by the acceleration dimension multiplied by the time dimension.
The Dimensional Analysis Calculator allows you to check whether an equation or relation is dimensionally consistent, that is, whether the dimensions of the quantities on the left side of the equation are equal to the dimensions of the quantities on the right side of the equation. This can help identify potential errors or omissions in the equation and ensure that the equation is physically correct.
With the Dimensional Analysis Calculator, you can enter an equation or relationship into a text entry and calculate the resulting dimension. The result is displayed in a text output and helps to check the consistency of the equation or relation.
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Advantages of our Calculator
Unlike other online calculators that use Java Script formulas, we prefer to use an Artificial Intelligence API capable of explaining the formulas and calculations to present the entire Dimensional Analysis completely instead of a simple result.
Another advantage of using Artificial Intelligence is its ability to understand any mistakes placed in the input form, thus allowing calculation even of incomplete or wrong equations.
Artificial Intelligence is also able to recognize different input forms, different types of equations and even parameters written in words instead of simple formulas. You can even ask for equations to be calculated without even having the equation, just put what you want in the input field.
Dimensional Analysis Calculator
How to use Dimensional Analysis
Here are some examples of how dimensional analysis can be used:
- Checking physical equations: Dimensional analysis is used to verify that physical equations are correct and consistent. For example, the kinetic energy equation, E = 1/2 * m * v^2, can be verified by dimensional analysis to ensure that energy (Joules) equals mass (kg) multiplied by velocity squared (m/ s)^2.
- Unit conversion: Dimensional analysis can be used to convert units of measure. For example, converting meters per second to kilometers per hour can be done by dimensional analysis, where 1 m/s = 3.6 km/h.
- System sizing: Dimensional analysis is used to size systems such as electrical circuits and hydraulic systems. For example, dimensional analysis can be used to determine the relationship between flow and pressure in a hydraulic system.
- Identification of physical constants: Dimensional analysis can be used to identify physical constants in an equation. For example, the gravitational constant G in Newton's law of universal gravitation, F = G * m1 * m2 / r^2, can be determined by dimensional analysis.
How is Dimensional Analysis done?
Dimensional analysis is based on the principle that physical quantities can be expressed as products of base units. For example, velocity can be expressed as the ratio of distance traveled to time: v = d/t. The units of velocity are therefore the unit of length divided by the unit of time.
The dimension of a physical quantity is represented by a combination of basic units. There are seven basic units in the International System of Units (SI): mass, length, time, electric current, temperature, amount of substance and luminous intensity.
Dimensional analysis is performed by dividing the equation or relation into terms, multiplying the dimensions of the units in each term, and checking that the dimensions of all quantities on the left side of the equation are equal to the dimensions of all quantities on the right side of the equation.
Dimensions of Basic Units for Dimensional Analysis
To perform the dimensional analysis, it is necessary to know the dimensions of the basic and derived units of the International System of Units (SI), as well as their conversion ratios.
Here are the seven SI base units and the physical quantities they measure:
| Unit | Dimension |
|---|---|
| meter (m) | length (L) |
| kilogram (kg) | mass (M) |
| second(s) | time (T) |
| ampere (A) | electric current (I) |
| kelvin (K) | temperature (Θ) |
| mol (mol) | amount of substance (N) |
| candle (cd) | luminous intensity (J) |
In addition to base units, there are other units of measure derived from base units. Here are some commonly used derived units and their corresponding dimensions:
| Unit | Dimension |
|---|---|
| newton (N) | MLT -2 |
| joule (J) | ML 2 T -2 |
| watt (W) | ML 2 T -3 |
| Paschal (Pa) | ML -1 T -2 |
| coulomb (C) | IT |
| volt (V) | ML 2 T -3 I -1 |
| ohm (Ω) | ML 2 T -3 I -2 |
Here is a table with some commonly used unit conversions:
| Unity 1 | Unit 2 | Conversion |
|---|---|---|
| meter (m) | kilometer (km) | 1 km = 1000 meters |
| meter (m) | centimeter (cm) | 1 m = 100 cm |
| meter (m) | millimeter (mm) | 1 m = 1000 mm |
| second(s) | millisecond (ms) | 1s = 1000 |
