What this calculator does
Tension is the pulling force transmitted through a rope, cable or string when it is taut. For a mass simply hanging at rest, tension equals weight: T = mg. If the mass is accelerating vertically instead, such as inside a lift, the tension also has to supply that extra force, giving T = m(g + a), where a is positive when accelerating upward and negative when accelerating downward.
A second common case is a mass supported by a single cable that runs at an angle rather than straight down, for example a weight held off to one side by a taut line. Here the cable has to supply the full weight through its vertical component alone, so the tension works out to T = mg / cos(θ), where θ is measured from vertical: the more the cable leans away from vertical, the harder it has to pull to hold the same weight up.
The formula
For a hanging mass, tension is mass times the sum of gravity and any vertical acceleration: T = m(g + a). At rest or moving at constant speed, a is zero and this reduces to T = mg. For a single cable at an angle from vertical, the cable's vertical component of tension must equal the weight, so T = mg / cos(θ); the horizontal component, T sin(θ), is the sideways pull that angle also produces.
| Term | Meaning |
|---|---|
| T | Tension, the pulling force in the rope or cable, in newtons. |
| m | Mass of the object being supported, in kilograms. |
| g | Gravitational acceleration, 9.80665 m/s². |
| a | Vertical acceleration of the mass, positive upward, zero if stationary or moving at constant speed. |
| θ | The angle of the cable measured from vertical, for the angled-cable case. |
The inputs explained
| Field | What to enter |
|---|---|
| Scenario | Choose a simple hanging mass (with optional vertical acceleration) or a mass held by a single cable at an angle from vertical. |
| Mass (kg) | The mass being supported by the rope or cable. |
| Vertical acceleration (0 if stationary or constant speed; positive = accelerating upward) (m/s²) | Vertical acceleration, if any. Leave at 0 for a stationary or constant-speed hanging mass; use a positive value for accelerating upward and a negative value for accelerating downward. |
| Angle of cable from vertical (°) | The angle the cable makes with the vertical, for the angled-cable scenario. |
When to use it
A weight hanging from a static rope
The simplest and most common case: a mass at rest or moving at constant speed, where tension is just weight, T = mg.
A lift or crane load accelerating vertically
When a suspended load speeds up or slows down vertically, the cable has to supply more or less than plain weight to produce that acceleration, which is why lift cables and crane lines are rated well above the static load they carry.
A single cable holding a weight off to one side
A cable that runs at an angle rather than straight down has to work harder to support the same weight, since only its vertical component is doing the lifting; this shows up in tent guy lines, cable-stayed supports and any load held away from directly below its anchor point.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How tension changes with mass for a stationary hanging load
A vertically hanging, stationary mass, across a range of masses.
How tension changes with cable angle for a fixed 10 kg mass
A fixed 10 kg mass, held by a cable at a range of angles from vertical.
| Angle from vertical | Tension | Horizontal component of tension |
|---|---|---|
| 0° | 98.07 N | 0.00 N |
| 10° | 99.58 N | 17.29 N |
| 20° | 104.36 N | 35.69 N |
| 30° | 113.24 N | 56.62 N |
| 40° | 128.02 N | 82.29 N |
| 50° | 152.56 N | 116.87 N |
Questions
What is the tension formula for a simple hanging weight?
For a mass at rest or moving at constant velocity, tension equals weight: T = mg. This is the baseline case that every other tension scenario builds on by adding acceleration or an angle.
How do I find tension when something is accelerating?
Add the acceleration to gravity before multiplying by mass: T = m(g + a), with acceleration taken as positive when directed upward. A load accelerating upward needs more tension than its static weight; one accelerating downward needs less, and in freefall (a = -g) tension drops to zero.
Why does an angled cable need more tension than a vertical one for the same weight?
A cable can only support weight through its vertical component. As the cable tilts away from vertical, that vertical component becomes a shrinking share of the total tension, so the cable has to pull harder overall, T = mg / cos(θ), just to keep supplying the same vertical support.
Can tension ever be negative?
No. A rope or cable can only pull, not push, so a negative result means the scenario is impossible as described, most often because a downward acceleration is larger than gravity itself, which would require the rope to push rather than pull and instead simply goes slack.
For the related force pressing an object into a surface rather than along a cable, see the normal force calculator.