The tidal volume is the volume of gas passing into or out of the lungs per breath (5-7ml/kg or approximately 500 ml in the average adult).
Minute volume is the volume of gas passing in or out of the lungs per minute. It is equal to the tidal volume multiplied by the number of breaths per minute.
Minute volume = Tidal volume X Respiratory rate = 500 ml X 10 rate = 5 liters (in the average adult)
Dead space is the part of the tidal volume that does not take part in ventilation. It could be considered wasted ventilation in that it serves no useful purpose where gaseous exchange is concerned. There are three types of dead spaces under anesthesia:

Anatomical dead space: This is the volume of gas that fills the respiratory passages but which is not involved in gas exchange. It extends from the nostrils and mouth down to, but not including, the alveoli. In the average adult this is about 150 ml (2ml/kg body weight). The anatomical dead space is reduced by tracheotomy and end tracheal intubation.

Physiological dead space: This includes all the air (that for various reasons) does not take part in gas exchange. It includes the anatomical dead space plus air in any of the alveoli into which the blood does not flow and any air in over distended alveoli where gaseous exchange is impaired. Physiological dead space is increased in lung disease.

Anesthetic dead space: The anesthetic dead space is the volume between the patient and the inflow of fresh gases into the "T piece". If a face mask is used, the dead space is increased considerably because part of the patient's tidal volume occupies the space under the mask and is hence wasted. The use of an endotracheal tube or a tracheotomy tube reduces the dead space.

Figure 3.9: Lung volume

In summery lung capacities are calculated by the following ways

VC = IRV + VT + ERV
VC = IC + ERV
TLC = VC + RV
TLC = IC + FRC
FRC = ERV + RV

Alveolar ventilation is that part of the tidal volume that actually takes part in gaseous exchange.
Tidal volume = dead space + alveolar ventilation 500 ml= 150 ml + 350 ml (in 75kg adult).

Expiratory reserve volume (ERV) is the amount of air that can be forcefully expired at the end of a normal expiration.
The inspiratory reserve volume is the extra volume of air that can be inspired over and above the normal tidal volume when the person inspires with full force; it is usually equal to about 3000 milliliters.
Residual volume (RV) is the amount of air remaining in the lungs at the end of a maximum forced expiration.
Functional residual capacity (FRC) is the volume of air in the lungs at the end of a normal expiration and is the sum of the ERV and the RV.It is important to the anesthetist because it contains a reservoir of oxygen (e.g. after pre-oxygenation and full nitrogen wash-out) which can maintain blood levels of oxygen during apnea. It is decreased by up to 25% in the supine position and also reduced in obesity, pregnancy and under anesthesia.
The inspiratory capacity equals the tidal volume plus the inspiratory reserve volume. This is the amount of air (about 3500 milliliters) a person can breathe in, beginning at the normal expiratory level and distending the lungs to the maximum amount.
Vital capacity is the greatest amount of air that can be expired after a person has breathed in as much as possible.
The total lung capacity is the maximum volume to which the lungs can be expanded with the greatest possible effort (about 5800 milliliters); it is equal to the vital capacity plus the residual volume.