How blood goes around the body

The work here is a “simplified teaching model”. It uses rough, round figures for the heart and blood vessels, and it is not medical diagnosis or health advice. Real numbers vary greatly between people, and with exercise and health.

How much the heart pumps in a minute

Each time the heart contracts it pushes out some blood. The amount per beat is called the stroke volume, and for an adult at rest (about 70 kg) about 70 mL is a rough guide. Sources give a range of 60 to 100 mL, and some give a larger figure. The resting heart rate is in the range of roughly 60 to 100 beats a minute. The amount pumped in a minute is stroke volume × heart rate.

• 70 mL × 70 beats = 4,900 mL, which is about 5 litres.
• Double the heart rate and the amount pumped in a minute doubles.
• With 70 mL per beat, 60 to 100 beats a minute gives about 4.2 to 7 litres a minute, inside the commonly quoted range of 4 to 8 litres.

This site’s program checked these calculations (blood-circulation/engine.test.ts).

Does blood go around once a minute?

The blood in the body is about 7 to 8% of body weight, roughly 5 litres for a 70 kg person (it changes with sex, age and build). The heart pumps about 5 litres a minute, so dividing gives about one minute. In this site’s program, 70 mL × 70 beats gives about 61 seconds. But this is only a rough estimate from a calculation. Not all blood takes the same route in the same time. Some goes round the short path through the lungs, and some takes finer, longer routes. It is wrong to say that all the blood goes round in exactly one minute.

Why speed changes from place to place

Blood moves at very different speeds in different vessels. As rough guides, about 20 to 40 cm per second in the aorta, much slower at 0.3 to 1 mm per second in capillaries, and about 10 to 20 cm per second in the large veins. Sources vary, and the speed in the aorta changes a lot with each heartbeat.

The continuity equation explains the difference. The flow (per second) equals the cross-sectional area times the speed. The amount of blood does not grow or shrink along the way, so where the total area is large the speed is low, and where it is small the speed is high. Each capillary is very thin, but when you add up all of them, the total cross-section is far bigger than the aorta’s. With the values used by this site’s model (capillaries 4,500 to 6,000 square centimetres in total, the aorta 3 to 5), the ratio is 900 to 2,000 times. For the same flow, the speed is 900 to 2,000 times smaller. Because the flow is slow, there is time for oxygen and nutrients to pass between the blood and the body.

Sources do not always agree on the area values, so read these figures as rough guides.

Two loops, lungs and body

Blood does not travel around a single loop. It travels around two loops. The pulmonary circulation goes from the right ventricle to the lungs and back to the left atrium. The systemic circulation goes from the left ventricle to the whole body and back to the right atrium. The two ventricles pump the same amount, because otherwise blood would pile up on one side. There is a common misunderstanding here. “Arteries carry oxygen-rich blood and veins carry oxygen-poor blood” is not always true. The pulmonary artery, going to the lungs, carries blood low in oxygen, and the pulmonary vein, returning from the lungs, carries blood rich in oxygen. Arteries and veins are told apart not by oxygen but by whether they carry blood away from the heart or back to it. This site’s program checks this point too.

Also, most of the blood (some sources say over 70%) is said to be in the veins. The veins act as a kind of reservoir.

Harvey’s calculation

In 1628 the English physician William Harvey published a book, De Motu Cordis (On the Motion of the Heart and Blood in Animals). In it he did a calculation. He deliberately underestimated: a heart chamber of about 43 mL, with an eighth of it, about 4.7 mL, pushed out per beat, and about 1,000 beats in 30 minutes. Even so, that is about 4.7 kg of blood in 30 minutes, and in a day far more than the body weighs. Harvey judged it hard to believe that so much blood could be made over and over inside the body, and concluded that the blood is not constantly made, but goes around the body. He is said to have backed this up with observations on snakes and fish and with experiments tying an arm.

One point needs care. It is not right to say that Harvey was the first to discover circulation. For the circulation through the lungs, Ibn al-Nafis (around 1242) and Servetus (a manuscript of 1546, printed in 1553) are said to have written about it earlier. Harvey’s achievement was to argue for circulation through the whole body in a convincing way, using numbers. Harvey also did not predict the thin vessels (capillaries) joining arteries to veins; he thought blood passed through tiny pores in the flesh. Capillaries were found in a later period.

How shaky is “100,000 km of capillaries”?

You may have heard that “capillaries laid end to end would be about 100,000 km, two and a half times round the Earth”. This figure is said to have weak support. It is traced to a book on capillaries from the 1920s by the Danish physiologist August Krogh (a Nobel Prize winner). The calculation there assumed “2,000 capillaries per square millimetre of muscle” and “50 kg of muscle”.

This site’s program reproduced the calculation (blood-circulation/engine.test.ts).

• With Krogh’s assumptions (2,000 per square millimetre, 50 kg of muscle) the result is about 100,000 km.
• With assumptions based on recent research (about 300 per square millimetre, about 23 kg of muscle) it is about 7,000 km, and that is for muscle only.
• The length is proportional to both the density and the muscle mass. Changing only the assumptions changes the answer by more than ten times.

A paper by researchers points out that Krogh’s density is much higher than present measurements in human muscle, and that 50 kg of muscle is an unusually large figure. It also says the 100,000 km refers to skeletal muscle only, for an imaginary single person, and not the whole body. So the true length is not well known. The famous figure is an estimate based on assumptions from the 1920s, and current research suggests it is considerably too large. This is also a good lesson about estimation: change the assumptions and the answer changes many times over. When you see a number, ask what assumptions it comes from.

Heartbeats in a lifetime

At 70 beats a minute, that is 100,800 beats a day. Keep that up for 80 years and it comes to about 2.94 billion. This site’s program checked the calculation. But heart rate changes with exercise, sleep and age, so this is a calculation with the assumption “about 70 beats a minute for 80 years”.

What they share

• Multiplying and dividing reveals how the body works: amount per beat × beats, blood volume ÷ amount pumped, area × speed.
• Read numbers together with their assumptions: even famous numbers change meaning depending on the assumptions behind them.
• Trace stories back to their sources: “who was first” and “how many kilometres” turn out not to be simple.

This is a simplified teaching model. It does not judge whether a heart rate is “normal” or “abnormal”. If you are worried about your body, please talk to a doctor.