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This work establishes some new inequalities to find error bounds for Maclaurin’s formulas in the framework of <i>q</i>-calculus. For this, we first prove an integral identity involving <i>q</i>-integral and <i>q</i>-derivative. Then, we use this new identity to prove some <i>q</i>-integral inequalities for <i>q</i>-differentiable convex functions. The inequalities proved here are very important in the literature because, with their help, we can find error bounds for Maclaurin’s formula in both <i>q</i> and classical calculus.