In Japanese, onomatopoeia (i.e., imitative or mimetic words) is frequently used in daily life conversation to express one's intuitive and sensitive feelings. Many onomatopoeic expressions are very similar to each other and their meanings seem to be vague and ambiguous so that it is hard to catch minute semantic differences among onomatopoeic expressions. However, we use onomatopoeia, even novel onomatopoeia, to express our subjective, intuitive and sensitive feelings in daily language use. Therefore, estimating information conveyed by onomatopoeia is inevitable in constructing a human-like intelligent communication system. In this study, we propose a system to estimate information conveyed by onomatopoeia based on Japanese sound symbolism. The existence of synesthetic associations between sounds and sensory experiences (sound symbolism) has been demonstrated over the decades. It is also known that the sensory-sound correspondence can be found not only in words referring to visual shapes, but also in those referring to tactile sensations. So our system quantifies images of inputted onomatopoeia using 43 adjective pair scales related to visual and tactile sensations. Our method hypothesizes that the impression created by an onomatopoeic expression could be predicted by the phonological characteristics of its constituent phonemes. To collect phonemic image data, we conducted a psychological experiment where 78 participants were asked to evaluate the impressions of 312 onomatopoeic expressions, which cover all kinds of Japanese phonemes, against 43 pairs of adjectives in seven-points SD scales. We applied the phonemic image data to our model, and calculated the impression values of each phoneme by making use of a mathematical quantification theory class I. This system estimates rich information conveyed by not only conventional but also newly created onomatopoeic expressions and differentiates among a variety of onomatopoeic expressions, which are frequently similar to each other. We conducted another psychological experiment in order to confirm the effectiveness of our system. Results showed that our system succeeded in evaluating information conveyed by onomatopoeia.