Introduction

Speed, distance and time calculations connect how fast you are travelling, how far you need to go and how long the journey will take.

The arithmetic is straightforward. The useful skill is choosing the right formula, keeping units consistent and working accurately under time pressure.

Start with the relationships below, then practise breaking calculations into smaller, familiar steps.

1. The three essential formulas

Identify the quantity you need to calculate before putting numbers into a formula.

• Speed: use groundspeed in knots (kt) for progress over the ground.
• Distance: use nautical miles (NM) with knots.
• Time: use hours with an hourly speed, or convert both to minutes.

One knot means one nautical mile per hour. Keep the same units throughout the calculation.

2. The SDT triangle

The triangle is a visual reminder of the three relationships.

3. Calculating distance

Distance = speed × time

4. Calculating speed

Speed = distance ÷ time

Dividing by half doubles the number. Dividing by a quarter multiplies it by four.

5. Calculating time

Time = distance ÷ speed

You can also work in nautical miles per minute: 120 ÷ 60 = 2 NM/min. Then 45 ÷ 2 = 22.5 minutes.

6. The 60 rule

Convert knots to nautical miles per minute by dividing by 60.

When time is in minutes: time = distance × 60 ÷ speed. For 80 NM at 160 kt, cancel 80 ÷ 160 to ½, then multiply by 60: 30 minutes.

7. Breaking down difficult calculations

Split the distance into parts that are easy to handle.

Estimate first. At about 3 NM/min, a journey of a little over 60 NM should take a little over 20 minutes.

8. Airspeed and groundspeed

Airspeed describes movement through the air. Groundspeed describes progress over the ground. Use groundspeed for the distance and time examples in this lesson.

A headwind reduces progress over the ground; a tailwind increases it. Wind at an angle needs a wind-triangle calculation rather than simply adding or subtracting the full wind speed.

9. Working under time pressure

1. Read the question and identify the unknown.
2. Check the units before calculating.
3. Use minutes-per-hour fractions or NM/min when convenient.
4. Estimate the size of the answer.
5. Write the unit with your answer.

Build accuracy first. Once the method feels familiar, practise with a timer.

10. Test your knowledge

Key takeaways

• Choose the formula from the unknown quantity.
• Keep knots, nautical miles and hours together.
• Convert knots to NM/min by dividing by 60.
• Use groundspeed when calculating progress over the ground.

1. Start with number sense

Break a number into hundreds, tens and ones. For 367 + 248, add 300 + 200, 60 + 40, then 7 + 8. Combine 500 + 100 + 15 = 615.

2. Follow the operation order

Work inside brackets first. Then do multiplication and division from left to right, followed by addition and subtraction from left to right.

3. Check division with multiplication

If 84 ÷ 7 = 12, multiplying 12 × 7 should give 84. An inverse operation is a quick way to check a result.

Test your knowledge

1. Recognise common equivalents

A decimal becomes a percentage when you multiply it by 100. A percentage becomes a decimal when you divide it by 100.

2. Find a fraction of a number

3. Break percentages into parts

4. Compare fractions

Use a common denominator: ⅔ = 8/12 and ¾ = 9/12, so ¾ is larger. Converting both to decimals is another useful approach.

Test your knowledge

1. Understand the parts

A ratio of 2:3 means two parts of one quantity for every three parts of another. There are five parts altogether.

2. Scale both quantities together

If three identical items cost 24, one costs 8 and five cost 40. Find a unit rate, then scale to the quantity you need.

3. Recognise a constant rate

At a constant 120 kt groundspeed, doubling the travel time doubles the distance. For a fixed distance, doubling the speed halves the travel time. State what remains fixed before deciding how quantities change.

Test your knowledge

1. Hours, minutes and seconds

One hour contains 60 minutes; one minute contains 60 seconds. Divide minutes by 60 to get hours. Multiply decimal hours by 60 to get minutes.

2. Nautical miles and knots

One nautical mile is exactly 1,852 metres (1.852 km). One knot is one nautical mile per hour. Do not mix nautical miles with statute miles or kilometres in a single calculation without converting.

3. Volume and mass

Litres measure volume; kilograms measure mass. Converting between them needs the fuel density. A burn rate in litres per hour must be paired with fuel in litres.

Test your knowledge

1. Round to friendly numbers

For 198 × 21, use 200 × 20 = 4,000 as a rough estimate. The exact answer, 4,158, should be close. An answer of 415.8 or 41,580 should prompt another check.

2. Know which way you rounded

3. Use simple bounds

For 95 ÷ 4, compare it with 80 ÷ 4 = 20 and 100 ÷ 4 = 25. Your answer must lie between 20 and 25.

An estimate checks plausibility. It does not replace an exact answer when the question asks for one.

Test your knowledge

1. Split difficult products

2. Use friendly multipliers

3. Cancel common factors

Before multiplying 80 × 60 ÷ 160, simplify 80 ÷ 160 to ½. The calculation becomes ½ × 60 = 30.

4. Choose a method you can check

A shortcut is useful only if it is reliable. Estimate the answer first and use a second method to check unfamiliar shortcuts while practising.

Test your knowledge

1. Connect fuel, rate and time

Use hours with an hourly rate. Pair litres with litres per hour, or kilograms with kilograms per hour.

2. Calculate fuel used

3. Calculate endurance

This is an arithmetic estimate. Real flight planning uses aircraft performance data and accounts for flight phases, conditions and applicable reserve requirements.

Test your knowledge

1. Read the compass

Bearings increase clockwise from a reference north. Keep the same reference throughout a question.

2. Follow left and right turns

Add a right turn; subtract a left turn. If a result is negative, add 360. If it is 360 or more, subtract 360 until it is in the range 000–359°.

3. Find the reciprocal

The reciprocal points in the opposite direction. Add 180° to bearings below 180°; subtract 180° from bearings of 180° or more. The reciprocal of 070° is 250°.

4. Heading, track and bearing

A heading is where the aircraft points. A track is its path over the ground. A bearing is a direction to or from a point. Wind can make heading and track differ.

Test your knowledge