Instruction-based image editing offers a powerful and intuitive way to manipulate images through natural language. Yet, relying solely on text instructions limits fine-grained control over the extent of edits. We introduce Kontinuous Kontext, an instruction-driven editing model that provides a new dimension of control over edit strength, enabling users to adjust edits gradually from no change to a fully realized result in a smooth and continuous manner. Kontinuous Kontext extends a state-of-the-art image editing model to accept an additional input, a scalar edit strength which is then paired with the edit instruction, enabling explicit control over the extent of the edit. To inject this scalar information, we train a lightweight projector network that maps the input scalar and the edit instruction to coefficients in the model's modulation space. For training our model, we synthesize a diverse dataset of image-edit-instruction-strength quadruplets using existing generative models, followed by a filtering stage to ensure quality and consistency. Kontinuous Kontext provides a unified approach for fine-grained control over edit strength for instruction driven editing from subtle to strong across diverse operations such as stylization, attribute, material, background, and shape changes, without requiring attribute-specific training.