Dimensional Equation Checker
Check whether a symbolic formula is dimensionally homogeneous. Set each variable's seven SI base-dimension exponents, then parse the equation locally. Addition and subtraction require equal dimensions; multiplication/division add/subtract exponents; powers scale them. Each side of = must match. Bare numbers are dimensionless, so even x + 0 is flagged under this strict convention. The checker finds inconsistencies; dimensional agreement alone cannot establish that a physical law is correct or convert numeric unit values.
Key features
- Positioned diagnostics for incompatible sums, unequal equation sides, unknown variables and malformed syntax
- Exact rational base exponents including negative and fractional powers; no JavaScript evaluation
- Dimensionless checks for sin, cos, tan, exp, ln and log; sqrt scales dimensions by one half
- Editable seven-base-dimension variable table with force, motion, error, trig and square-root examples
- Local JSON project restore plus JSON and CSV analysis downloads
How to use
- Choose an example or enter one equation with exactly one = and explicit multiplication such as m*a.
- Give every variable a name and exponents of M, L, T, I, Θ, N and J. Zero means no contribution; fractions such as -3/2 are accepted.
- Analyze the equation. Read the dimensions of both sides and each evaluated subexpression.
- Use the highlighted character position and left/right dimensions to fix mismatches, then export a report or project.
Use cases
- Catch an accidental mass-plus-acceleration term
- Check a kinematic equation with nested products
- Verify a trig argument is dimensionless
- Inspect fractional or negative dimension exponents
Frequently asked questions
Does a valid result prove the equation?
No. Dimensional homogeneity is necessary for an ordinary physical equality, but many incorrect formulas also have matching dimensions. Coefficients, signs, boundary conditions and empirical assumptions are not checked.
Which dimensions can I enter?
M mass, L length, T time, I electric current, Θ thermodynamic temperature, N amount of substance and J luminous intensity. Enter exponents as integers or rational strings such as -3/2; the all-zero exponent vector is shown as 1.
What operations are supported?
Explicit +, -, *, /, ^, parentheses and unary signs, plus single-argument sin/cos/tan/exp/ln/log and sqrt. Function arguments other than sqrt must be dimensionless. Unknown functions, implicit multiplication and nonnumeric powers are rejected.
How are numeric constants treated?
Every bare numeric literal is dimensionless, including zero. Thus adding bare 0 to a dimensional variable is flagged; use an explicitly dimensioned variable for a dimensioned constant.
Can it convert units or check values?
No. It checks exponents of symbolic base dimensions, not numerical values, SI prefixes or offset units such as Celsius. The separate unit converter handles value conversion.
Where does my equation go?
Analysis runs in this browser. Downloaded report/project files are local; importing project JSON does not submit it to an application server.
Privacy
The equation and variable dimensions remain in this browser tab. Analysis and file creation run locally.
Comments & questions