Find travel distance from speed and time, or straight-line distance between two points — with every step shown. Free and mobile-friendly.
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Pick a mode first. **Speed & time mode** answers “how far?” from a steady speed: enter the speed, choose its unit (km/h, mph, or m/s), enter the travel time in hours, and choose the unit you want the answer in. Press **Calculate** and the tool multiplies speed by time, converts units behind the scenes, and shows the step-by-step arithmetic so you can check it.
**Coordinate mode** answers “how far apart?” for two points on a flat map: enter x₁, y₁, x₂, y₂ and press Calculate. The tool applies the Pythagorean distance formula and shows each substitution. Use **Reset** any time to restore the defaults (60 km/h for 2.5 hours; points (1,2) and (4,6)).
Everything runs in your browser — no sign-up, no data sent anywhere — and the layout works on phones, so you can settle a road-trip argument from the passenger seat.
Who relies on it? Commuters estimating arrival times, teachers demonstrating the Pythagorean theorem on real maps, hikers converting trail time into kilometers, dispatchers quoting delivery windows, and students checking homework — anyone whose day involves the question “how far?”
Distance is one of the most-used quantities in science, and it carries two closely related meanings. In travel, distance is the length of the path you actually covered: the odometer reading after a drive, the trail length on a hike. In mathematics, distance is the straight-line separation between two points — the shortest possible route, even if you never travel it.
Both meanings share the same unit family: meters, kilometers, miles, feet. The SI unit is the meter. A useful mental ladder: a doorway is about 1 m wide, a city block is roughly 100 m, a mile is 1,609 m, and a marathon is 42,195 m. Holding a few of these anchors makes every estimate easier to sanity-check.
The two calculator modes mirror the two meanings: speed × time gives path distance at constant speed, while the coordinate formula gives straight-line distance. Confusing them is the classic error — a winding mountain road can be twice the straight-line distance on the map.
The speed–time formula is a rearrangement of the definition of speed (v = d ÷ t). It assumes speed stays constant; if speed varies, it gives the distance for the average speed instead. Units must agree: speed in km/h times time in hours gives kilometers. Mixing minutes with km/h is the most common unit slip — convert minutes to hours first (divide by 60).
The coordinate formula is the Pythagorean theorem in disguise: the horizontal and vertical gaps form a right triangle, and the distance is its hypotenuse. It works in any consistent unit — pixels on a screen, meters on a site plan — because it only compares positions.
Your family drives at a steady 90 km/h for 3 hours and 20 minutes. How far? First convert the time: 20 minutes is ⅓ hour, so t = 3.333 h. Then d = 90 × 3.333 = 300 km. The calculator does the unit bookkeeping if you enter 3.333 directly — or enter 200 minutes as 3.333 hours after dividing by 60.
A second scenario: two delivery depots sit at map coordinates (2, 5) and (9, 14) in kilometers. The straight-line distance is √((9−2)² + (14−5)²) = √(49 + 81) = √130 ≈ 11.4 km. The delivery van’s actual route will be longer — this number is the optimistic lower bound planners use for coverage zones.
Mixing time units. Multiplying km/h by minutes gives a nonsense number 60× too small. Convert to hours first.
Path vs. straight line. Navigation apps report road distance; the coordinate formula reports as-the-crow-flies. They answer different questions.
Forgetting the average-speed caveat. d = v × t with a varying speed needs the average speed, not the top speed.
Unit drift in coordinates. If x is in meters and y in kilometers, the formula breaks. Convert first, then compute.
Rounding too early. Keep 3–4 decimals through the steps and round only the final answer.
Runner: 12 km/h for 45 minutes → t = 0.75 h, d = 12 × 0.75 = 9 km.
Flight: 800 km/h for 2 h 15 min → t = 2.25 h, d = 1,800 km.
Map: points (0,0) and (3,4) → d = √(9+16) = 5 exactly — the famous 3-4-5 triangle.
Screen: pixels (100,200) to (400,600) → d = √(300² + 400²) = 500 px.
A bakery promises delivery within a 20-minute drive and wants to draw its zone on a map. At an average city speed of 30 km/h, 20 minutes (⅓ h) covers 10 km of road distance. But roads wind: planners use a detour factor of about 1.3, so the straight-line radius to advertise is 10 ÷ 1.3 ≈ 7.7 km. Drawing that circle with the coordinate mode — depot at the center, boundary points 7.7 km out — gives a defensible, honest delivery map.
Distance has two faces: path length (speed × time) and straight-line separation (coordinate formula) — pick the one your question asks.
Keep units consistent: km/h pairs with hours, m/s pairs with seconds.
The coordinate formula is Pythagoras: d = √((x₂−x₁)² + (y₂−y₁)²).
Convert, compute, then round — never round mid-calculation.
Distance wears different costumes in different professions, but the mathematics stays the same. Astronomers measure cosmic distances in light-years — the distance light travels in one year, about 9.46 trillion km — because kilometers become unwieldy past the solar system. The nearest star, Proxima Centauri, is 4.24 light-years away, a number you can grasp far more easily than 40 trillion km.
Surveyors live on the coordinate formula. A total station measures angles and one distance, then triangulates every other point — centuries of land boundaries rest on d = √((x₂−x₁)² + (y₂−y₁)²) applied thousands of times. Modern GPS does the same in three dimensions, solving for your position from satellite distances.
Sports scientists track player distance with wearable GPS: a soccer midfielder covers 10–12 km per match, mostly in short bursts. Coaches compare that path distance against tactical expectations to manage fatigue — the same speed × time relation, sampled 10 times per second and summed.
Logistics planners distinguish relentlessly between the two distance meanings. Straight-line distance sets the service-area circle; road-network distance sets fuel budgets and driver shifts. Confusing them underestimates costs by the detour factor — typically 1.2 to 1.4 in cities, higher in mountains.
Try these, then check the answers — show your unit conversions explicitly.
1. A train travels at 110 km/h for 2 h 45 min. Distance? Answer: t = 2.75 h; d = 302.5 km.
2. Points A(−3, 7) and B(5, 1). Distance? Answer: √((8)² + (−6)²) = √100 = 10.
3. A cyclist covers 60 km at 25 km/h. Time in minutes? Answer: t = 2.4 h = 144 min.
4. A plane flies 450 miles at 180 mph. Distance in km? Answer: t = 2.5 h; d = 450 mi = 724 km.
5. Two warehouses at (0, 0) and (12, 5) km. A drone flies straight; a truck drives 1.35× the straight distance. How far does each travel? Answer: drone 13 km; truck ≈ 17.6 km.
Humans measured distance long before they had numbers for it: the cubit (forearm length), the foot, the pace (a Roman double-step, ~1.48 m — the ancestor of the mile, mille passus, a thousand paces). These body-based units were convenient and hopelessly inconsistent — a king’s foot differed from a farmer’s.
The meter was born in revolutionary France as one ten-millionth of the Earth’s quadrant, a unit belonging to no king’s body. Surveyors Delambre and Méchain spent seven years triangulating from Dunkirk to Barcelona to define it — the coordinate distance formula, applied across a continent. Their bar was slightly off (they misjudged the Earth’s flattening), but the principle held: a universal, reproducible standard.
Today the meter is defined by light itself: the distance light travels in 1/299,792,458 of a second. Distance measurement has come full circle — from body parts, through planetary surveying, to a fundamental constant of nature. Every time this calculator multiplies speed by time, it stands on that lineage.
The Distance Calculator has two modes: (1) travel distance from constant speed via d = v × t with automatic unit conversion (km/h, mph, m/s → km, miles, meters); (2) straight-line coordinate distance via d = √((x₂−x₁)² + (y₂−y₁)²). Key facts: match time units to speed units (minutes ÷ 60); path distance ≥ straight-line distance; with varying speed the formula gives average-speed distance.
For constant speed: d = v × t (distance = speed × time). For two points (x₁,y₁) and (x₂,y₂): d = √((x₂−x₁)² + (y₂−y₁)²).
Multiply them with matching units: 60 km/h × 2.5 h = 150 km. If time is in minutes, divide by 60 first to get hours.
Distance is the total path length traveled (always positive). Displacement is the straight-line change in position, with direction — it can be zero for a round trip.
Subtract the x-coordinates, subtract the y-coordinates, square both differences, add them, and take the square root. For (1,2) and (4,6): √((3)²+(4)²) = 5.
No. Distance is a scalar quantity — a length — so it is always zero or positive. A negative sign belongs to displacement or position, which carry direction.
Meters (SI), kilometers, miles, feet, and nautical miles for aviation and shipping. Convert everything to one unit before calculating.
GPS computes straight-line distances between satellite positions and your receiver using the 3D version of the coordinate formula, then road-routing layers convert those into driving distances.
Maps often show straight-line or simplified route distances. Your odometer measures the actual winding path, which is always equal or longer.
Cite this page as: Distance Calculator. Sigma Calculator. Retrieved October 11, 2026, from https://sigmacalculator.net/math-calculators/distance-calculator/
Last updated: October 11, 2026