Cardiac output (Q) is correctly expressed as: (a) Q = HR + SV (b) Q = HR × SV (c) Q = SV ÷ HR (d) Q = SV - HR

Cardiac output (Q) is correctly expressed as: (a) – Class 12 Physical Education

Concept understanding — Cardiac Output Formula

Cardiac Output: The Heart's Delivery System

Think of your heart as the delivery engine of your body. Every cell needs oxygen and nutrients to survive, and every cell produces waste that must be carried away. The heart's job is to pump blood — the delivery vehicle — through a closed network of pipes (arteries, veins, capillaries) to reach every tissue. But how much blood does the heart actually move in a given time? That quantity is called cardiac output.

The Core Idea

Cardiac output is simply the volume of blood the heart pumps out in one minute. It tells you how hard the heart is working to meet the body's demands. If the body needs more oxygen — say, during exercise or stress — cardiac output rises. If the heart is weak or damaged, cardiac output falls, and the body struggles to get enough supply.

Two factors determine cardiac output:

Stroke volume — the amount of blood pumped out by one ventricle in a single beat (about 70 mL at rest in a healthy adult)
Heart rate — the number of beats per minute (about 72 beats per minute at rest)

Cardiac output is the product of these two: stroke volume multiplied by heart rate. At rest, this works out to roughly 5 litres per minute — which is nearly the entire blood volume of an average adult. That means your heart pumps all your blood through your body once every minute.

Note

The heart has two sides — right and left — but cardiac output refers to the output of one ventricle (usually the left ventricle, which pumps blood to the whole body). Both ventricles pump the same volume per minute; otherwise blood would pool on one side.

Why It Matters

Cardiac output is not a fixed number. It changes constantly to match the body's needs. When you run, your muscles demand more oxygen, so your heart rate rises and stroke volume increases — cardiac output can climb to 20–25 litres per minute in a trained athlete. When you sleep, demand drops, and cardiac output falls.

Doctors and physiologists care about cardiac output because it reveals how well the heart is functioning. A low cardiac output can indicate heart failure, where the pump is too weak to meet demand. A high cardiac output can occur in conditions like anaemia or hyperthyroidism, where the body demands more blood flow even at rest.

Several factors influence cardiac output:

Physical activity — increases both heart rate and stroke volume
Emotional state — fear or excitement raises heart rate
Body temperature — fever increases metabolic demand and cardiac output
Blood volume — if you lose blood, stroke volume drops and cardiac output falls
Nervous system signals — the autonomic nervous system speeds up or slows down the heart …

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Cardiac output is blood pumped per minute. Stroke volume is blood pumped per beat, and heart rate is beats per minute. Multiplying them gives volume per minute, so Q = HR × SV — option (b).

Concept understanding — what each term means

Term	Symbol	Definition	Unit	Typical resting adult value
Heart rate	HR	Number of contractions of the heart in one minute	beats/min	~72 beats/min
Stroke volume	SV	Volume of blood ejected by the left ventricle in one contraction	mL/beat	~70 mL/beat
Cardiac output	Q	Volume of blood pumped out by the heart in one minute	mL/min or L/min	~5 L/min

Cardiac output is the single number that tells you how much oxygen-carrying blood the working muscles can actually be supplied with. It is therefore the central variable of the cardiovascular system in sport.

Why the formula is a product

Q = HR \times SV

The cleanest way to see it is by unit analysis — let the units derive the formula for you:

beats/minute(HR) × mL/beat(SV) = mL/minute = Q

The word "beat" cancels, leaving millilitres per minute — which is exactly the definition of cardiac output. No other operation can do this: addition and subtraction require the two quantities to have the same unit (they do not), and division would leave "beats" squared in the denominator.

Worked check with resting values

Take a resting adult: HR = 72 beats/min and SV = 70 mL/beat.
Substitute into the formula: Q = 72 × 70.
Compute: Q = 5040 mL/min.
Convert to litres: Q = 5040/1000 = 5.04 L/min ≈ 5 L/min.

That matches the accepted resting cardiac output of about 5 litres per minute — the whole blood volume of the body circulated roughly once every minute. The formula is confirmed by the number it produces.

What happens in exercise

Q = HR × SV

tells you there are exactly two routes to raising cardiac output during exercise, and endurance training exploits both:

HR rises — from ~72 up towards the maximum heart rate.
SV rises — a bigger venous return stretches the ventricle, which contracts more forcefully (the Frank–Starling relationship), so more blood leaves per beat.

Because they multiply, a trained athlete can reach a cardiac output several times the resting value. Suppose an athlete works at HR = 180 beats/min with a trained SV = 160 mL/beat:

Q = 180 × 160 = 28,800 mL/min = 28.8 L/min

Important

The same equation explains resting bradycardia in trained athletes. Training enlarges the ventricle, so SV rises. But the body only needs about 5 L/min at rest. Since Q = HR × SV must still equal ~5 L/min, a larger SV forces a lower resting HR. With SV = 100 mL/beat, the required rate is HR = 5000 ÷ 100 = 50 beats/min. A low resting pulse in an endurance athlete is a sign of an efficient, powerful heart — not a weak one.

Refuting the other options …

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Q.Cardiac output (Q) is correctly expressed as:

Concept understanding — what each term means

Why the formula is a product

Worked check with resting values

What happens in exercise

Refuting the other options …

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