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There can be no conversion. A linear metre is a measure of length in 1-dimensional space (or, if given the width, the measure of area in 2-dimensional space) while gsm is a measure of planar density. The units of the first are [L] (or implied [L^2]) while those gsm are [ML^-2]. The two measure different things and, according to basic principles of dimensional analysis, any attempt at conversion from one to the other is fundamentally flawed.

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Q: How to convert gsm to linear meter?
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