Explore More Tools
Mastering Motion Equations
Understanding the relationship between Speed, Time, and Distance
Whether you are planning a road trip, training for a marathon, or solving a physics problem, the relationship between Speed, Time, and Distance is fundamental. Our calculator simplifies this with unit conversions and interactive visuals, but understanding the core concepts gives you a deeper intuition for motion.
The Magic Triangle
The DST Triangle is the easiest way to remember the formulas. The horizontal line represents division, and the vertical line represents multiplication.
- DDistance = Speed × TimeCover 'D' at the top, multiply the bottom two.
- SSpeed = Distance ÷ TimeCover 'S', divide top by bottom right.
- TTime = Distance ÷ SpeedCover 'T', divide top by bottom left.
D is always on top. S and T are interchangeable at the bottom.
Common Speeds Reference
| Object / Action | Approx. Speed (km/h) | Approx. Speed (mph) | Notes |
|---|---|---|---|
| Human Walking | 5 km/h | 3.1 mph | Average adult pace |
| Usain Bolt | 44.72 km/h | 27.8 mph | Top recorded speed |
| Cheetah | 100 - 120 km/h | 60 - 75 mph | Fastest land animal |
| Commercial Jet | 880 - 926 km/h | 550 - 575 mph | Cruising speed |
| Sound (Air) | 1,235 km/h | 767 mph | At sea level, 20°C |
| Light (Vacuum) | 1.08 × 10⁹ km/h | 6.71 × 10⁸ mph | Universal speed limit |
Travel Planning
Calculating driving times between cities or flight durations. Essential for logistics and navigation.
Sports Pacing
Runners and cyclists use "pace" (time per distance), which is simply the inverse of speed.
Physics
The foundation of kinematics. Understanding D=ST is a prerequisite for more complex motion laws.
Frequently Asked Questions
What is the formula for Speed, Time, and Distance?
The fundamental formula is Distance = Speed × Time (D = S × T). From this, you can derive: Speed = Distance ÷ Time (S = D/T) and Time = Distance ÷ Speed (T = D/S).
How do I use the DST Triangle?
The DST Triangle is a visual memory aid. 'D' is at the top, with 'S' and 'T' at the bottom. To use it, cover the letter you want to find. If you cover D, you see S and T next to each other (multiply). If you cover S, you see D over T (divide).
How do I convert km/h to mph?
To convert kilometers per hour (km/h) to miles per hour (mph), multiply by approximately 0.621371. For example, 100 km/h ≈ 62 mph. Our calculator handles these conversions automatically.
What is the difference between average speed and instantaneous speed?
Instantaneous speed is your speed at a specific moment (like what a speedometer shows). Average speed is the total distance traveled divided by the total time taken, accounting for stops and speed changes.
How do I calculate time if I know speed and distance?
Use the formula T = D ÷ S. Divide the Distance by the Speed. For example, to travel 100 km at 50 km/h: 100 ÷ 50 = 2 hours.
What are the common units for speed?
Common units include: Kilometers per hour (km/h) for driving in most countries, Miles per hour (mph) in the US/UK, Meters per second (m/s) in physics, and Knots in aviation/marine navigation.
How fast is the speed of sound?
The speed of sound in dry air at 20°C is approximately 343 meters per second (m/s), or about 1,235 km/h (767 mph). This varies with temperature and medium.
How fast is the speed of light?
The speed of light in a vacuum is exactly 299,792,458 meters per second (approx 300,000 km/s or 186,000 mi/s). It is the universal speed limit.
How do I calculate speed from distance and time?
Use the formula S = D ÷ T. Divide the total Distance by the Time taken. Example: Traveling 120 miles in 2 hours means Speed = 120 ÷ 2 = 60 mph.
Why is velocity different from speed?
Speed is a scalar quantity (magnitude only), while velocity is a vector quantity (magnitude AND direction). '50 mph' is speed; '50 mph North' is velocity.
How do I calculate distance traveled?
Use D = S × T. Multiply your average Speed by the Time. Example: Walking at 5 km/h for 3 hours means Distance = 5 × 3 = 15 km.
What is a Knot?
A Knot is a unit of speed equal to one nautical mile per hour (approx 1.852 km/h or 1.15 mph). It is strictly used in meteorology, maritime, and air navigation.
Can distance be negative?
Distance is a scalar quantity and is always non-negative. Displacement (a vector) can be negative depending on the coordinate system, but distance traveled is always ≥ 0.
How to convert minutes to hours for the formula?
Divide the number of minutes by 60. For example, 30 minutes = 30 ÷ 60 = 0.5 hours. Always ensure your time unit matches the speed unit's time component (e.g., hours for km/h).
What is uniform speed?
Uniform (or constant) speed means covering equal distances in equal intervals of time. If a car's speedometer stays exactly at 60 km/h, it is moving at uniform speed.