Loading page
About this tool
Compare the base-dimension exponents on each side of an equation to flag mismatched, dimensionally invalid terms.
The Dimensional Consistency Checker compares the two sides of an equation as base-dimension vectors — exponents of mass M, length L, time T, current I, temperature Θ, amount N and luminous intensity J — and reports a match or an exponent-by-exponent mismatch. You reduce each side to base dimensions yourself and enter them as tokens like "M1 L1 T-2"; the tool then lines the exponents up in a table and counts the disagreements. It is a bookkeeping check on dimensional homogeneity, not an algebra parser or a unit converter.
Open Dimensional Consistency Checker on AltFTool — it loads instantly in your browser.
Type each side's exponents into 'Left-side dimension vector' and 'Right-side dimension vector' as tokens like M1 L1 T-2.
Adjust 'Allowed base symbols' (default M,L,T,I,Θ,N,J) or load the 'Force = mass × acceleration' preset.
Read the verdict — 'Dimension vectors match' or 'Dimensionally inconsistent' — with a per-dimension Match/Mismatch table.
The table shows left and right exponents per base symbol, so a mismatch points at T or L directly instead of at the equation as a whole.
M, L, T, I, Θ, N and J are compared, so electrical, thermal and photometric expressions are covered, not just mechanics.
The result states outright that matching dimensions are necessary but not sufficient for a physically correct equation.
An equation is dimensionally consistent when every term has the same exponents on each base dimension — Newton's second law works because both force and mass × acceleration reduce to M1 L1 T-2. If one side is L1 and the other L1 T-1, the equation is wrong no matter what the numbers say.
Mass (M), length (L), time (T), electric current (I), thermodynamic temperature (Θ), amount of substance (N) and luminous intensity (J) — the dimensional counterparts of the seven SI base units kilogram, metre, second, ampere, kelvin, mole and candela. Every derived quantity is a product of powers of these.
As symbol-and-exponent pairs separated by spaces, with negative exponents written directly: energy is "M1 L2 T-2", pressure is "M1 L-1 T-2", and a dimensionless quantity is left blank or entered as zero exponents. Anything you omit is treated as exponent 0.
Not necessarily. Dimensional analysis cannot see dimensionless factors, so an expression that should carry a ½, a 2π, or a drag coefficient passes the check while still being numerically wrong. It also cannot catch a sign error — treat a match as ruling out one whole class of mistakes, not as a proof.