Formula Used
Dimensional analysis replaces quantities with fundamental dimension powers. Matching powers confirm compatible units and equations. Different powers reveal errors before numerical work begins.
How to Use
Select the required calculation mode first. Enter values, formulas, units, or variable definitions carefully. Press calculate to view dimensions, checks, and detailed steps.
- Choose conversion, lookup, formula, equation, unknown, or Pi analysis.
- Enter expressions using supported symbols and numeric exponents.
- Review the result, validation status, and base-unit representation.
- Copy, print, or export the completed calculation.
Example Data
| Mode | Example input | Expected result |
|---|---|---|
| Conversion | 36 km/h to m/s | 10 m/s |
| Lookup | Pressure | M L^-1 T^-2 |
| Equation check | s = u*t + 0.5*a*t^2 | Dimensionally consistent |
| Unknown solver | F = k*x | [k] = M T^-2 |
| Buckingham Pi | rho, v, D, mu | One Reynolds-type group |
Supported Syntax
Use stars for multiplication and slashes for division. Parentheses control grouping, while carets define numeric powers. Variable names may contain letters, numbers, and underscores.
Frequently Asked Questions
What is dimensional analysis?
Dimensional analysis studies relationships between measurable physical quantities. It represents quantities using fundamental dimensions and powers. This method checks equations and supports reliable unit conversions.
Which base dimensions are supported?
The calculator supports seven standard SI base dimensions. These cover mass, length, time, current, and temperature. Amount and luminous intensity are also fully included.
Can compound units be entered?
Yes, compound unit expressions are accepted directly. Multiplication, division, parentheses, and numeric exponents are supported. Examples include kg/m^3, N*m, and J/(kg*K).
How does equation checking work?
The calculator evaluates dimensions on both equation sides. Added terms must also share identical dimensional formulas. Matching final vectors confirm dimensional consistency for the equation.
Can it solve unknown dimensions?
Yes, multiplicative equations can isolate one unknown dimension. Known variable dimensions must be supplied before calculation. The solver returns dimensions and equivalent SI base units.
What is a dimensionless quantity?
A dimensionless quantity has zero powers for every dimension. Ratios often become dimensionless after complete cancellation. Reynolds, Mach, and friction coefficients are familiar examples.
How are Pi groups generated?
The calculator builds a variable dimension matrix. Row reduction finds its rank and nullspace basis. Each nullspace vector defines one independent dimensionless Pi group.
Why are unit symbols case-sensitive?
Case distinguishes symbols with different scientific meanings. For example, watts and webers cannot share notation. Accurate capitalisation prevents unintended parsing and conversion errors.
Can results be exported?
Results can be copied, printed, or downloaded. CSV export supports spreadsheets and calculation records. PDF export creates a portable summary for later reference.