What this tool covers
Use a single screen to confirm unit algebra, show substitutions for students, and derive Buckingham Π groups for experiments.
- Expand any unit expression to the SI base vector and compute the scale factor k.
- Analyse equations term by term, ensuring additions are homogeneous and function arguments are dimensionless.
- Build Π groups by solving the null space of the dimension matrix with integer exponents.
- Share results through CSV export or a copyable URL that stores the current state.
Interactive calculator
Choose a mode, enter your variables, then review the annotated steps before exporting results.
Results
How it’s calculated
FAQ
How do I convert between compound units with this tool?
Select the Unit mode, enter the compound unit expression such as L or km/h, and optionally supply a target unit. The tool expands the expression to the SI base vector, reports the scale factor k, and if a target is provided it confirms the dimensions match and gives the conversion, for example 1 L = 0.001000 m^3.
What does the equation consistency check validate?
Provide the equation and each variable’s unit. The checker expands every variable, computes dimensions for the left- and right-hand sides, and ensures additions and subtractions are between homologous dimensions. It also enforces that trig/exp/log arguments are dimensionless, so expressions such as exp(g*t) raise a flag while sin(v/v0) passes.
How are Buckingham Π groups generated?
In the Π-groups mode, list the variables and their units. The tool forms the 7×n dimension matrix, computes its null space, and returns an integer basis for the dimensionless products. For a pendulum with T, L, and g it produces Π = g^1·T^2·L^-1, matching textbook derivations.
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