BiologyPhysiologyA-Level
AQACISCECambridgeNESAOCREdexcelWJECCBSE

Stroke Volume

Volume of blood pumped out of the left ventricle per heartbeat.

Understand the formulaSee the free derivationOpen the full walkthrough
Open Full WalkthroughTry Calculator

This public page keeps the free explanation visible and leaves premium worked solving, advanced walkthroughs, and saved study tools inside the app.

Core idea

Overview

Stroke volume represents the amount of blood pumped by the left ventricle in a single contraction, serving as a vital metric for ventricular efficiency. It is derived by dividing the total cardiac output by the heart rate, effectively measuring the volume of blood ejected per cardiac cycle.

When to use: This formula is used in clinical cardiology and exercise physiology to determine the heart's pumping capacity per beat. It assumes a steady state where cardiac output and heart rate are accurately measured over the same time interval.

Why it matters: It helps clinicians distinguish between changes in heart performance due to heart rate variations versus changes in the heart's actual muscular strength or volume capacity. High stroke volumes are often seen in endurance athletes, while low stroke volumes can indicate cardiac dysfunction or dehydration.

Symbols

Variables

CO = Cardiac Output, HR = Heart Rate, SV = Stroke Volume

CO
Cardiac Output
ml/min
HR
Heart Rate
bpm
SV
Stroke Volume
ml

Walkthrough

Derivation

Formula: Stroke Volume

The volume of blood ejected by the left ventricle per heartbeat.

  • Measured using cardiac output and heart rate data.
1

Derive Stroke Volume from Cardiac Output:

Cardiac output (CO) is the product of stroke volume and heart rate (HR). Rearranging gives SV = CO ÷ HR.

2

Alternatively from Ventricular Volumes:

Stroke volume equals end-diastolic volume (EDV) minus end-systolic volume (ESV).

Note: Normal resting SV ≈ 70 mL. During exercise SV can exceed 150 mL.

Result

Source: AQA / OCR A-Level Biology — Mass Transport in Animals

Free formulas

Rearrangements

Solve for CO

Make co the subject

Exact symbolic rearrangement generated deterministically for co.

Difficulty: 2/5

Solve for HR

Make hr the subject

Exact symbolic rearrangement generated deterministically for hr.

Difficulty: 3/5

The static page shows the finished rearrangements. The app keeps the full worked algebra walkthrough.

Visual intuition

Graph

The graph of Stroke Volume (SV) against Heart Rate (HR) is a hyperbolic curve, representing an inverse relationship where SV decreases as HR increases, assuming Cardiac Output remains constant. The curve approaches both axes as asymptotes, as SV cannot be zero and HR must be positive.

Graph type: hyperbolic

Why it behaves this way

Intuition

Imagine the heart as a pump delivering a continuous flow (cardiac output); stroke volume is the amount of fluid pushed out with each individual pump stroke, and heart rate is how many strokes occur per minute.

SV
Volume of blood ejected from the left ventricle per heartbeat.
This is the 'amount of blood per push' from the heart. A higher value means the heart is more effective at moving blood with each individual contraction.
CO
Total volume of blood pumped by the left ventricle per minute.
This represents the 'total blood flow' from the heart over a minute, indicating the overall circulatory demand being met.
HR
Number of heartbeats per minute.
This is simply 'how many times the heart beats' in a minute, reflecting the frequency of cardiac contractions.

Signs and relationships

  • HR (in the denominator): Heart rate is in the denominator because stroke volume is defined as the volume of blood per *beat*. For a given total cardiac output (CO), if the heart beats more frequently (higher HR), then each individual beat must

Free study cues

Insight

Canonical usage

This equation requires consistent time units for cardiac output and heart rate to ensure stroke volume is expressed as volume per beat.

Common confusion

A common mistake is using inconsistent time units for cardiac output and heart rate (e.g., CO in L/min and HR in beats/second), which will lead to an incorrect stroke volume unit or value.

Unit systems

SVml/beat - Stroke volume is the resulting volume of blood ejected per cardiac cycle, typically reported in milliliters per beat.
COml/min - Cardiac output is the total volume of blood pumped by the heart per unit time. Its time unit (e.g., minutes) must match the time unit of heart rate.
HRbeats/min - Heart rate is the number of heartbeats per unit time. The 'beats' is a count and effectively dimensionless for unit cancellation, leaving a time unit in the denominator. Its time unit (e.g., minutes)

Ballpark figures

  • Quantity:
  • Quantity:
  • Quantity:

One free problem

Practice Problem

Practice Problem 1

An athlete has a measured cardiac output of 5250 mL/min and a resting heart rate of 75 beats per minute. Calculate the stroke volume.

Cardiac Output5250 ml/min
Heart Rate75 bpm

Solve for: sv

Hint: Divide the total volume pumped per minute by the number of beats in that same minute.

Practice Problem 2

During a stress test, a patient's stroke volume is determined to be 80 mL per beat with a heart rate of 110 beats per minute. What is the patient's cardiac output in mL/min?

Stroke Volume80 ml
Heart Rate110 bpm

Solve for: co

Hint: Rearrange the formula to solve for Cardiac Output: CO = SV ×HR.

Practice Problem 3

A patient has a cardiac output of 4800 mL/min and a stroke volume of 60 mL. Calculate the patient's heart rate in beats per minute.

Cardiac Output4800 ml/min
Stroke Volume60 ml

Solve for: hr

Hint: Rearrange the formula to solve for heart rate: HR = CO / SV.

The full worked solution stays in the interactive walkthrough.

Where it shows up

Real-World Context

In a biology investigation involving Stroke Volume, Stroke Volume is used to calculate the sv value from Cardiac Output and Heart Rate. The result matters because it helps turn a changing quantity into a total amount such as area, distance, volume, work, or cost.

Study smarter

Tips

  • Check that Cardiac Output is in mL/min if you want the result in mL.
  • A typical resting stroke volume for an adult is around 70 mL.
  • Heart rate must be in beats per minute for the standard calculation.

Avoid these traps

Common Mistakes

  • Multiplying instead of dividing.
  • Convert units and scales before substituting, especially when the inputs mix ml/min, bpm, ml.
  • Interpret the answer with its unit and context; a percentage, rate, ratio, and physical quantity do not mean the same thing.

Common questions

Frequently Asked Questions

The volume of blood ejected by the left ventricle per heartbeat.

This formula is used in clinical cardiology and exercise physiology to determine the heart's pumping capacity per beat. It assumes a steady state where cardiac output and heart rate are accurately measured over the same time interval.

It helps clinicians distinguish between changes in heart performance due to heart rate variations versus changes in the heart's actual muscular strength or volume capacity. High stroke volumes are often seen in endurance athletes, while low stroke volumes can indicate cardiac dysfunction or dehydration.

Multiplying instead of dividing. Convert units and scales before substituting, especially when the inputs mix ml/min, bpm, ml. Interpret the answer with its unit and context; a percentage, rate, ratio, and physical quantity do not mean the same thing.

In a biology investigation involving Stroke Volume, Stroke Volume is used to calculate the sv value from Cardiac Output and Heart Rate. The result matters because it helps turn a changing quantity into a total amount such as area, distance, volume, work, or cost.

Check that Cardiac Output is in mL/min if you want the result in mL. A typical resting stroke volume for an adult is around 70 mL. Heart rate must be in beats per minute for the standard calculation.

References

Sources

  1. Wikipedia: Stroke volume
  2. Wikipedia: Cardiac output
  3. Wikipedia: Heart rate
  4. Guyton and Hall Textbook of Medical Physiology
  5. Boron and Boulpaep Medical Physiology
  6. AQA / OCR A-Level Biology — Mass Transport in Animals