A method for monitoring exothermic reactions in a reactor, in which one or more starting materials react exothermically to give at least one product, and at least one gas is present in the reactor during operation as intended or during a runaway, comprising the following process steps: A) measurement and storage of an initial temperature and an initial pressure in the reactor, B) calculation of the amount of products and starting materials present in the reactor from an energy balance, C) calculation of a maximum pressure raise that occurs on stepwise reaction of the amount of starting materials present in relation to a calculated starting pressure, which is higher than the initial pressure, wherein, in order to calculate the maximum pressure raise that occurs (step C), the amount of starting materials present is divided into k part-amounts Δn, and the following steps are carried out k times: a) calculation of a temperature change ΔT which arises in the reactor and an amount of starting materials and products remaining in the reactor on reaction of a part-amount Δn of starting materials in the exothermic reaction, b) calculation of an intermediate temperature arising from the temperature change ΔT, c) calculation of an intermediate pressure in the reactor using a phase equilibrium calculation into which the intermediate temperature, the amount of starting materials and products which remains, and the volume of the reactor are entered as given quantities, d) storage of the intermediate pressure as the starting pressure p 1 in the first run through steps a) to d), e) calculation of an adiabatic pressure increase as the difference between the intermediate pressure and the starting pressure, and f) storage of the adiabatic pressure increase as the maximum pressure raise if this exceeds a value previously stored as the maximum pressure rise. and D) calculation of a runaway pressure from the maximum pressure raise that occurs, calculated in step C), and the measured initial pressure stored in step A). A) measurement and storage of an initial temperature and an initial pressure in the reactor, B) calculation of the amount of products and starting materials present in the reactor from an energy balance, C) calculation of a maximum pressure raise that occurs on stepwise reaction of the amount of starting materials present in relation to a calculated starting pressure, which is higher than the initial pressure, wherein, in order to calculate the maximum pressure raise that occurs (step C), the amount of starting materials present is divided into k part-amounts Δn, and the following steps are carried out k times: a) calculation of a temperature change ΔT which arises in the reactor and an amount of starting materials and products remaining in the reactor on reaction of a part-amount Δn of starting materials in the exothermic reaction, b) calculation of an intermediate temperature arising from the temperature change ΔT, c) calculation of an intermediate pressure in the reactor using a phase equilibrium calculation into which the intermediate temperature, the amount of starting materials and products which remains, and the volume of the reactor are entered as given quantities, d) storage of the intermediate pressure as the starting pressure p 1 in the first run through steps a) to d), e) calculation of an adiabatic pressure increase as the difference between the intermediate pressure and the starting pressure, and f) storage of the adiabatic pressure increase as the maximum pressure raise if this exceeds a value previously stored as the maximum pressure rise. and a) calculation of a temperature change ΔT which arises in the reactor and an amount of starting materials and products remaining in the reactor on reaction of a part-amount Δn of starting materials in the exothermic reaction, b) calculation of an intermediate temperature arising from the temperature change ΔT, c) calculation of an intermediate pressure in the reactor using a phase equilibrium calculation into which the intermediate temperature, the amount of starting materials and products which remains, and the volume of the reactor are entered as given quantities, d) storage of the intermediate pressure as the starting pressure p 1 in the first run through steps a) to d), e) calculation of an adiabatic pressure increase as the difference between the intermediate pressure and the starting pressure, and f) storage of the adiabatic pressure increase as the maximum pressure raise if this exceeds a value previously stored as the maximum pressure rise. and D) calculation of a runaway pressure from the maximum pressure raise that occurs, calculated in step C), and the measured initial pressure stored in step A).