<p>In this study, we derive new dynamic Hardy-type inequalities within the framework of delta calculus on time scales. Utilizing fundamental tools such as the chain rule, Hölder’s inequality, and integration by parts, we establish a new class of Hardy-type inequalities that unify and extend the existing results. In particular, when the time scale <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {T}= \mathbb {R}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="double-struck">T</mi> <mo>=</mo> <mi mathvariant="double-struck">R</mi> </mrow> </math></EquationSource> </InlineEquation>, our results reduce to integral inequalities previously introduced by Sroysang, whereas for <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathbb {T}= \mathbb {Z}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="double-struck">T</mi> <mo>=</mo> <mi mathvariant="double-struck">Z</mi> </mrow> </math></EquationSource> </InlineEquation>, we obtain new discrete inequalities.</p>