tirepressure.app is a free bike tire pressure calculator that gives you personalized front and rear tire pressures for road bikes, TT and triathlon bikes, gravel bikes, and mountain bikes. It focuses on accuracy and ease of use: a research-based pressure model powered by a handful of inputs.
Your recommended bike tire pressures are calculated from a number of inputs: total system weight, tire size and type, riding surface, and riding speed. Front and rear pressures are calculated separately, since that weight is not distributed evenly between the two wheels. The resulting pressures aim to minimize rolling resistance for your setup.
Most riders run their tires too hard, assuming a firmer tire rolls faster. On real roads, it doesn't: an overinflated tire can bounce over bumps instead of absorbing them, which costs you speed as well as grip and comfort. Lower, correctly chosen pressures can be faster in practice, as long as you stay above the point where the tire starts to bottom out on the rim.