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Direct comparison of areal and profile roughness measurement values is notadvisable due to fundamental differences in the measurement techniques. Howeverresearchers may wish to compare between laboratories with differing equipment,or against literature values. This paper investigates how well the profilearithmetic mean average roughness, $R_a$, approximates its areal equivalent$S_a$. Simulated rough surfaces and samples from the ETOPO1 global relief modelwere used. The mean of up to 20 $R_a$ profiles from the surface were comparedwith surface $S_a$ for 100 repeats. Differences between $\bar{R_a}$ and $S_a$fell as the number of $R_a$ values averaged increased. For simulated surfacesmean % difference between $\bar{R_a}$ and $S_a$ was in the range 16.06% to3.47% when only one $R_a$ profile was taken. By averaging 20 $R_a$ values mean% difference fell to 6.60% to 0.81%. By not considering $R_a$ profiles parallelto the main feature direction (identified visually), mean % difference wasfurther reduced. For ETOPO1 global relief surfaces mean % difference was in therange 52.09% to 22.60% when only one $R_a$ value was used, and was 33.22% to9.90% when 20 $R_a$ values were averaged. Where a surface feature directioncould be identified, accounting for reduced the difference between $\bar{R_a}$and $S_a$ by approximately 5% points. The results suggest that taking the meanof between 3 and 5 $R_a$ values will give a good estimate of $S_a$ on regularor simple surfaces. However, for some complex real world surfaces discrepancybetween $\bar{R_a}$ and $S_a$ are high. Caveats including the use of filtersfor areal and profile measurements, and profile alignment are discussed.

A simulated comparison between profile and areal surface parameters: $R_a$ as an estimate of $S_a$