Coaching Centre
Heart rate
Heart rate in beats per minute from a count over a shorter time, estimated maximum heart rate, target training zones, recovery rate, and how much blood the heart pumps.
Your heart rate is a rate in the everyday sense: beats per minute, written bpm. Coaches use it to set training, doctors use it to check health, and fitness watches show it all day. The maths is mostly scaling a short count up to a full minute, then taking percentages.
Measuring heart rate
Counting for a full minute is slow, so people usually count for a shorter time and scale up. A minute is $4$ lots of $15$ seconds, so multiply a $15$-second count by $4$. For $10$ seconds multiply by $6$, and for $20$ seconds by $3$.
Ella counts $19$ beats in $15$ seconds. What is her heart rate?
Press Count for 15 s on the Mystery pulse and count the flashes yourself, then compare with the counter. Switch to Set the pulse, choose $74$ bpm and count again: why can't a $15$-second count give exactly $74$? Then set your own age and an effort of $70\%$ and read your target heart rate.
Maximum heart rate and training zones
$\text{maximum heart rate} \approx 220 - \text{age}$
$\text{target heart rate} = \text{percentage} \times \text{maximum heart rate}$
A common guide is that moderate exercise is about $50\%$ to $70\%$ of maximum heart rate and vigorous exercise is about $70\%$ to $85\%$. The $220 - \text{age}$ rule is only an estimate for an average person: real maximum heart rates vary by $10$ bpm or more either way.
Find the vigorous training zone ($70\%$ to $85\%$) for a $17$-year-old.
Recovery and blood flow
Recovery rate measures how fast the heart rate falls after exercise. A fitter person's heart rate drops faster. It is a rate of change: bpm lost per minute.
Straight after a run, Kai's heart rate is $168$ bpm. Two minutes later it is $120$ bpm. Find the average recovery rate.
A resting heart beats $72$ times a minute and pumps about $70$ mL of blood with each beat. How many litres does it pump in a minute, and how many beats is that in a day?
Your turn
A $45$-year-old wants to exercise at $60\%$ of maximum heart rate. In $10$ seconds she counts $18$ beats. Is she above or below her target?
Show the working
Maximum: $220 - 45 = 175$ bpm. Target: $0.6 \times 175 = 105$ bpm. Her rate: $18 \times 6 = 108$ bpm, so she is slightly above her target.
$19$ beats are counted in $15$ seconds. What is the heart rate in bpm?
$19 \times 4 = 76$ bpm.
$26$ beats are counted in $20$ seconds. What is the heart rate in bpm?
$60 \div 20 = 3$, so $26 \times 3 = 78$ bpm.
Estimate the maximum heart rate of a $17$-year-old.
$220 - 17 = 203$ bpm.
What is $70\%$ of the maximum heart rate of a $17$-year-old?
$0.7 \times 203 = 142.1$ bpm.
A $15$-second count is used to find a heart rate. Missing one beat changes the answer by:
Each beat counted is multiplied by $4$, so one missed beat is $4$ bpm.
A heart rate falls from $168$ bpm to $120$ bpm in $2$ minutes. What is the average recovery rate, in bpm per minute?
$(168 - 120) \div 2 = 48 \div 2 = 24$.
A heart beats $72$ times a minute and pumps $70$ mL per beat. How many litres per minute is that?
$72 \times 70 = 5040$ mL, and $5040 \div 1000 = 5.04$ L.
Why is $220 - \text{age}$ only an estimate?
The rule fits a large group on average. An individual's measured maximum can be well above or below it.
Exam style: A $45$-year-old exercises at $60\%$ of maximum heart rate. What is the target, in bpm?
Maximum $= 220 - 45 = 175$. Target $= 0.6 \times 175 = 105$ bpm.
Exam style: She counts $18$ beats in $10$ seconds. Compared with her target, she is:
$18 \times 6 = 108$ bpm, and $108 - 105 = 3$, so she is $3$ bpm above her target.